optimal decay rates for solutions of a nonlinear wave equation with localized nonlinear dissipation of unrestricted growth and critical exponent source terms under mixed boundary conditions abstract this article investigates optimal decay rates for solutions to a semilinear hyperbolic equation with localized interior damping and a source term both dissipation and the source are fully nonlinear and the growth rate of the source map may include critical exponents for sobolev s embedding h 1 l 2 besides continuity and monotonicity no growth or regularity assumptions are imposed on the damping we analyze the system in the presence of neumann type boundary conditions including the mixed cases dirichlet neumann robin the damping affects a thin layer a collar near a portion of the boundary to cope with the lack of control on the remaining section we develop a special method that accounts for propagation of the energy estimates from the dissipative region onto the entire domain the neumann system does not satisfy the lopatinski condition in higher dimensions hence the study of energy propagation in the absence of damping near the neumann segment requires special geometric considerations

global well posedness for nonlinear wave equations with supercritical source and damping terms abstract we prove the global well posedness of weak solutions for nonlinear wave equations with supercritical source and damping terms on a three dimensional torus t 3 of the prototype u t t u u t m 1 u t u p 1 u x t t 3 r u 0 u 0 h 1 t 3 l m 1 t 3 u t 0 u 1 l 2 t 3 where 1 p min 2 3 m 5 3 m notably p is allowed to be larger than 6

long time dynamics of kirchhoff wave models with strong nonlinear damping we study well posedness and long time dynamics of a class of quasilinear wave equations with a strong damping we accept the kirchhoff hypotheses and assume that the stiffness and damping coefficients are functions of the l2 norm of the gradient of the displacement we prove the existence and uniqueness of weak solutions and study their properties for a wide class of nonlinearities which covers the case of possible degeneration or even negativity of the stiffness coefficient and the case of a supercritical source term our main results deal with global attractors for strictly positive stiffness factors we prove that in the natural energy space endowed with a partially strong topology there exists a global finite dimensional attractor in the non supercritical case this attractor is strong in this case we also establish the existence of a fractal exponential attractor and give conditions that guarantee the existence of a finite number of determining functionals

plate models with state dependent damping coefficient and their quasi static limits abstract we study long time dynamics of a class of plate models with a state dependent damping coefficient and their quasi static limits we first present the problem in abstract form and then prove the existence of finite dimensional global attractors and their upper semicontinuity in the quasi static limit i e in the case when the mass density of plate tends to zero our proofs involve a recently developed method based on compensated compactness and quasi stability estimates as an application we consider the nonlinear kirchhoff von karman and berger plate models with different types of boundary conditions and damping coefficients our results can be also applied to the nonlinear wave equations in an arbitrary dimension

global smooth solutions and stabilization of nonlinear elastodynamic systems with locally distributed dissipation we consider the existence of global solutions of the nonlinear elastodynamic system with a locally distributed damping in a bounded domain we assume that the energy function satisfies the strong ellipticity condition at the zero equilibrium the local dissipation is in the form a x u where the nonnegative function a x is only positive on a small portion of the domain we show the existence of global smooth solutions when initial data are small in particular we obtain the exponential decay of the energy which implies the exponential stabilization of the system by internal feedback

existence of a solution of the wave equation with nonlinear damping and source terms abstract we study the nonlinear wave equation involving the nonlinear damping term u t u t m 1 and a source term of type u u p 1 for 1 p m we prove a global existence theorem with large initial data for 1 m p a blow up result is established for sufficiently large initial data

a bootstrap procedure for high resolution velocity analysis a method is given for further improving velocity estimates derived from high resolution velocity analysis in conventional velocity analysis a set of tentative velocities is used to apply a normal moveout nmo correction to a set of spatio temporal windows the coherence measure is evaluated for each velocity and finally the velocity estimate is retrieved from the peak of the coherence measure because analytical expressions for velocity uncertainties are difficult to derive i propose an intensive statistical procedure the bootstrap method to assess the accuracy of the velocity estimate in the bootstrap method i create a data sample by randomly drawing seismic traces with replacement from a window of the common midpoint gather cmp next i calculate the velocity that maximizes the coherence measure for each bootstrap realization the variation of this velocity provides a means to compute standard errors i also use the bootstrap method to construct an average coherence measure and a kernel density estimator of the velocity that maximizes the coherence the average coherence exhibits an important attenuation of spurious events while retaining enough resolution to model reflections properly with similar moveout curves the latter is illustrated with synthetic and field data examples

global existence and nonexistence for nonlinear wave equations with damping and source terms we consider an initial boundary value problem for a nonlinear wave equation in one space dimension the nonlinearity features the damping term u m 1 u t and a source term of the form u p 1 u with m p 1 we show that whenever m p then local weak solutions are global on the other hand we prove that whenever p m and the initial energy is negative then local weak solutions cannot be global regardless of the size of the initial data

stable and unstable sets for the cauchy problem for a nonlinear wave equation with nonlinear damping and source terms for the cauchy problem for the nonlinear wave equation with nonlinear damping and source terms we define stable and unstable sets for the initial data we prove that if during the evolution the solution enters into the stable set the solution is global and we are able to estimate the decay rate of the energy if during the evolution the solution enters into the unstable set the solution blows up in finite time

spatio temporal spectral analysis by eigenstructure methods this paper presents new algorithms for estimating the spatio temporal spectrum of the signals received by a passive array the algorithms are based on the eigenstructure of the covariance and spectral density matrices of the received signals they allow partial correlation between the sources and thus are applicable to certain kinds of multipath problems simulation results that illustrate the performance of the new algorithms are presented

propagation of boundary cr foliations and morera type theorems for manifolds with attached analytic discs abstract we prove that homologically nontrivial generic smooth 2 n 1 parameter families of analytic discs in c n n 2 attached by their boundaries to a cr manifold test cr functions in the following sense if a smooth function on analytically extends into any analytic discs from the family then the function satisfies tangential cr equations on in particular we give an answer theorem 1 to the following long standing open question so called strip problem earlier solved only for special families mainly for circles given a smooth one parameter family of jordan curves in the plane and a function f admitting holomorphic extension inside each curve must f be holomorphic on the union of the curves we prove for real analytic functions and arbitrary generic real analytic families of curves that the answer is yes if no point is surrounded by all curves from the family the latter condition is essential we generalize this result to characterization of complex curves in c 2 as real 2 manifolds admitting nontrivial families of attached analytic discs theorem 4 the main result implies fairly general morera type characterization of cr functions on hypersurfaces in c 2 in terms of holomorphic extensions into three parameter families of attached analytic discs theorem 2 one of the applications is confirming in real analytic category the globevnik stout conjecture theorem 3 on boundary values of holomorphic functions it is proved that a smooth function on the boundary of a smooth strictly convex domain in c n extends holomorphically inside the domain if it extends holomorphically into complex lines tangent to a given strictly convex subdomain the proofs are based on a universal approach namely on the reduction to a problem of propagation from the boundary to the interior of degeneracy of cr foliations of solid torus type manifolds theorem 2 2

systems of nonlinear wave equations with damping and supercritical boundary and interior sources utt u g1 ut f1 u v vtt v g2 vt f2 u v in a bounded domain r with robin and dirichlet boundary conditions on u and v respectively the nonlinearities f1 u v and f2 u v are with supercritical exponents representing strong sources while g1 ut and g2 vt act as damping in addition the boundary condition also contains a nonlinear source and a damping term by employing nonlinear semigroups and the theory of monotone operators we obtain several results on the existence of local and global weak solutions and uniqueness of weak solutions moreover we prove that such unique solutions depend continuously on the initial data

analyticity on rotation invariant families of curves let be a rotation invariant family of smooth jordan curves contained in a the open unit disc in c for each t let dt be the simply connected domain bounded by t we present various conditions which imply that if is a continuous function on a such that for every fe the function f t has a continuous extension to dt which is analytic in dr then is analytic in a

a high resolution weighted ab semblance for dealing with amplitude variation with offset phenomenon abstractvelocity analysis is an essential step in seismic reflection data processing the conventional and fastest method to estimate how velocity changes with increasing depth is to calculate semblance coefficients traditional semblance has two problems low time and velocity resolution and an inability to handle amplitude variation with offset avo phenomenon although a method known as the ab semblance can arrive at peak velocities in the areas with an avo anomaly it has a lower velocity resolution than conventional semblance we have developed a weighted ab semblance method that can handle both problems simultaneously we have developed two new weighting functions to weight the ab semblance to enhance the resolution of velocity spectra in the time and velocity directions in this way we increase the time and velocity resolution while eliminating the avo problem the first weighting function is defined based on the ratio between the first and the second singular values of the time window to improve

analyticity on translates of a jordan curve let be a domain in which is symmetric with respect to the real axis and whose boundary is a real analytic simple closed curve translate vertically to get where is such that we prove that if is a continuous function on such that for each the function has a continuous extension to which is holomorphic on then is holomorphic on

global existence to the initial boundary value problem for a system of semilinear wave equations abstract we prove the global existence of finite energy and h 2 solutions for a system of nonlinear wave equations in a bounded domain one equation of the system has a dissipative term while another equation has no dissipative mechanism to derive the delicate a priori estimates we employ a loan method

mixed problem for some semi linear wave equation with a nonhomogeneous condition on considere le probleme aux valeurs limites et initiales suivant u tt u xx u t sign u t 0 x t 0 1 0 t u x 0 t g t u 1 t 0 u x 0 u 0 x u t x 0 u 1 x avec 0 1 avec u 0 h 1 0 1 u 1 dans l 2 0 1 et g t dans l 2 0 t un theoreme d existence globale et d unicite est demontre

regularity theory of hyperbolic equations with non homogeneous neumann boundary conditions ii general boundary data abstract this paper studies the regularity of solutions of general mixed second order time dependent hyperbolic problems of neumann type in a previous paper i lasiecka and r triggiani ann mat pura appl iv clvii 1990 285 367 using pseudo differential calculus we have provided sharp regularity results of the solutions and their traces when the non homogeneous data are in l 2 now we complement this study by providing a regularity when the non homogeneous data are more regular than as well as less regular than l 2 in contrast with our previous paper a functional analytic approach based on the l 2 results of our previous paper is used throughout

existence uniqueness and blowup for hyperbolic equations with nonstandard growth conditions in this paper we consider the following problem utt u b x t u x t 2u f x t x t qt 0 t u x 0 u0 x ut x 0 u1 x 0 x u t 0 t 0 t under conditions 0 b t b x t b t 0 b t b x t b t 1 t x t t 1 t x t t we study the existence and uniqueness of weak and strong solutions we prove the blowup of nonnegative solutions also we consider the blowup effect for a more generalized problem utt lu f x t u inqt u x 0 u0 x in ut x 0 u1 x in u 0on t where ll is the linear elliptic operator lu di aij x dju ai x u a0 x u lu di aij x dju ai x u a0 x u and the right hand side has the form f x t u k 1nbk x t u k x t 1 i nkci x t di s t u i s t 1ds with bk 0bk 0 ci 0ci 0 di 0di 0

local and global wellposedness of weak solutions for the wave equation with nonlinear boundary and interior sources of supercritical exponents and damping abstract we consider the wave equation with interior and boundary nonlinear sources and damping and we are interested in local and global wellposedness of finite energy solutions the main difficulty is represented by the fact that the lopatinski condition fails to hold unless the dim 1 and thus the analysis of the boundary nonlinearities becomes a subtle issue

global existence and open loop exponential stabilization of weak solutions for nonlinear schrodinger equations with localized external neumann manipulation abstract in this paper we consider the nonlinear schrodinger equations nls with focusing defocusing interior source and possibly nonlinear damping on a bounded regular domain in the euclidean space moreover it is assumed that the solutions are subject to external neumann boundary manipulation on one portion of the boundary our aim is to obtain global existence of the weak solutions under various assumptions on the sign of the source and powers of the nonlinearities in the case of a linear damping we also prove that solutions decay exponentially under the assumption that the neumann type control at the boundary decays in a similar manner

blow up of a hyperbolic equation of viscoelasticity with supercritical nonlinearities abstract we investigate a hyperbolic pde modeling wave propagation in viscoelastic media under the influence of a linear memory term of boltzmann type and a nonlinear damping modeling friction as well as an energy amplifying supercritical nonlinear source u t t k 0 u 0 k s u t s d s u t m 1 u t u p 1 u in 0 t u x t u 0 x t in 0 where is a bounded domain in r 3 with a dirichlet boundary condition the relaxation kernel k is monotone decreasing and k 1 we study blow up of solutions when the source is stronger than dissipations i e p max m k 0 under two different scenarios first the total energy is negative and the second the total energy is positive with sufficiently large quadratic energy this manuscript is a follow up work of the paper 30 in which hadamard well posedness of this equation has been established in the finite energy space the model under consideration features a supercritical source and a linear memory that accounts for the full past history as time goes to which is distinct from other relevant models studied in the literature which usually involve subcritical sources and a finite time memory

on a navier stokes allen cahn model with inertial effects abstract a mathematical model describing the flow of two phase fluids in a bounded container is considered under the assumption that the phase transition is influenced by inertial effects the model couples a variant of the navier stokes system for the velocity u with an allen cahn type equation for the order parameter relaxed in time in order to introduce inertia at the microscopic level the resulting model is characterized by second order material derivatives which constitute the main difficulty in the mathematical analysis in order to obtain a tractable problem a viscous relaxation term is then included in the phase equation the mathematical results consist in existence of weak solutions in 3d and under additional assumptions existence and uniqueness of strong solutions in 2d a partial characterization of the long time behavior of solutions is also given and in particular some issues related to dissipation of energy are discussed

attractors for kirchhoff s equation with a nonlinear damping coefficient abstract we consider kirchhoff s equation with a nonlinear damping coefficient depending on the displacement the equation is proven to generate a dissipative semigroup possessing both compact global and exponential attractors

a note on a strongly damped wave equation with fast growing nonlinearities a strongly damped wave equation including the displacement depending nonlinear damping term and nonlinear interaction function is considered the main aim of the note is to show that under the standard dissipativity restrictions on the nonlinearities involved the initial boundary value problem for the considered equation is globally well posed in the class of sufficiently regular solutions and the semigroup generated by the problem possesses a global attractor in the corresponding phase space these results are obtained for the nonlinearities of an arbitrary polynomial growth and without the assumption that the considered problem has a global lyapunov function

global well posedness of solutions for fourth order dispersive wave equation with nonlinear weak damping linear strong damping and logarithmic nonlinearity abstract to understand the characteristics of dynamical behavior especially the kinetic evolution for logarithmic nonlinearity we aim to study the global well posedness of nonlinear fourth order wave equations with logarithmic source term where the dispersive the nonlinear weak damping and linear strong damping are taken into account based on the potential well method the main ingredient of this paper is to construct several conditions for initial data leading to the solution global existence or infinite time blow up with subcritical initial energy moreover we extend the results to the critical initial energy which is realized by introducing scaling technique finally surrounding the blow up at arbitrarily high initial energy we compare and discuss the research program stemming from two different strategies in the first one it is assumed that the blow up result is bound to the original logarithmic source by weakening the dispersive dissipative structure while the second one is based on the nonlinear wave equation with complete dispersive dissipative structure but the logarithmic source is replaced by an enhanced version through these two strategies we explain the mechanism of these two structures respectively and establish two kinds of sufficient conditions for initial data leading to high energy blow up

local hadamard well posedness for nonlinear wave equations with supercritical sources and damping abstract we consider the wave equation with supercritical interior and boundary sources and damping terms the main result of the paper is local hadamard well posedness of finite energy weak solutions the results obtained 1 extend the existence results previously obtained in the literature by allowing more singular sources 2 show that the corresponding solutions satisfy hadamard well posedness conditions during the time of existence this result provides a positive answer to an open question in the area and it allows for the construction of a strongly continuous semigroup representing the dynamics governed by the wave equation with supercritical sources and damping

global solutions to a structure acoustic interaction model with nonlinear sources abstract this article focuses on a structural acoustic interaction system consisting of a semilinear wave equation defined on a smooth bounded domain r 3 which is strongly coupled with a berger plate equation acting only on a flat part of the boundary of in particular the source terms acting on the wave and plate equations are allowed to have arbitrary growth order we employ a standard galerkin approximation scheme to establish a rigorous proof of the existence of local weak solutions in addition under some conditions on the parameters in the system we prove such solutions exist globally in time and depend continuously on the initial data

signal and traveltime parameter estimation using singular value decomposition abstractsignal detection and traveltime parameter estimation can be performed by computing a coherence function in a data window centered around a traveltime function defined by its parameters we used singular value decomposition of the data matrix not eigendecomposition of a covariance matrix to review the most commonly used coherence measures this resulted in a new reduced semblance coefficient defined from the first eigenimage assuming that the signal amplitude was the same on all data channels as in classical semblance in a second signal model the time signal was constant on each channel but the amplitude changed then the semblance coefficient is the square of the first singular value divided by the energy of the data two normalized crosscorrelation coefficients derived from the first eigenimage can also be used as a coherence measure the normalized crosscorrelation of the spatial singular vector with a vector with all elements equal to one and the normalized crosscorrelation of the tem

weak solutions and blow up for wave equations of p laplacian type with supercritical sources this paper investigates a quasilinear wave equation with kelvin voigt damping utt pu ut f u in a bounded domain 3 and subject to dirichlet boundary conditions the operator p 2 p 3 denotes the classical p laplacian the nonlinear term f u is a source feedback that is allowed to have a supercritical exponent in the sense that the associated nemytskii operator is not locally lipschitz from w01 p into l2 under suitable assumptions on the parameters we prove existence of local weak solutions which can be extended globally provided the damping term dominates the source in an appropriate sense moreover a blow up result is proved for solutions with negative initial total energy

on the initial boundary problem for fourth order wave equations with damping strain and source terms abstract in this paper we study the global existence and blow up of solutions to the fourth order equations u t t u t 2 u u i 1 n x i i u x i f u x t 0 where 0 under appropriate assumptions on the initial data and parameters in the above equation we establish two results on blow up of solutions with arbitrary initial energy e 0 also by using a potential well we show the global existence of solutions for the fourth order wave equation with some i s and f s especially it is proved that the energy decays exponentially as t

the relationship between semblance and eigenstructure velocity estimators this short presentation gives for the first time a formulation of the semblance coefficient in terms of data covariance matrix eigenstructure because the high resolution wavefront or spectral eigenstructure methods have received so much interest over the past decade it is necessary to analytically tie the conventionally used semblance produce to eigenstructure thereby allowing the seismic signal analyst an opportunity to relate the various displays of velocity spectra using more than visual appearance the eigenstructure form of semblance is compared to a number of the now well known eigenstructure based spectral estimators that separate signal and noise vector subspaces because of the inclusion of noise space energy in the coherence measure conventional semblance does not have the resolving power of the newer methods we suggest an enhanced semblance based on the signal and noise subspace separation concept a brief simulation verifies the visual improvement in the velocity spectrum obtained from

exponential energy decay of solutions of viscoelastic wave equations abstract in this paper we consider the nonlinear viscoelastic equation u t t u 0 t g t u d u t u p 1 u in 0 with initial conditions and dirichlet boundary condition under some appropriate assumption on g by introducing a potential well we establish the global existence result for the equation above furthermore we investigate explicit exponential energy decay of the viscoelastic wave equation under the potential well

global existence and blow up of solutions to systems of nonlinear wave equations with degenerate damping and source terms abstract we focus on the global well posedness of the system of nonlinear wave equations u t t u d u k e v l u t m 1 u t f 1 u v v t t v d v e u v t r 1 v t f 2 u v in a bounded domain r n n 1 2 3 with dirichlet boundary conditions the nonlinearities f 1 u v and f 2 u v act as a strong source in the system under some restriction on the parameters in the system we obtain several results on the existence of local solutions global solutions and uniqueness in addition we prove that weak solutions to the system blow up in finite time whenever the initial energy is negative and the exponent of the source term is more dominant than the exponents of both damping terms

on holomorphic extensions from spheres in ℂ2 a theorem of rudin states that if b is the open unit ball in n n 1 if 0 if is the family of all complex lines in n at a distance from the origin and if f c b is such that for every the function f b has a continuous extension to b which is holomorphic in b then f has a continuous extension to b which is holomorphic in b in this paper we show that when n 2 the theorem still holds if is replaced by a considerably smaller family

fast acoustic velocity tomography of focusing operators abstracta 2d velocity model was estimated by tomographic imaging of overlapping focusing operators that contain one way traveltimes from common focus points to receivers in an aperture along the earth s surface the stability and efficiency of convergence and the quality of the resulting models were improved by a sequence of ideas we used a hybrid parameterization that has an underlying grid upon which is superimposed a flexible pseudolayer model we first solved for the low wavenumber parts of the model approximating it as constant velocity pseudo layers then we allowed intermediate wavenumbers allowing the layers to have linear velocity gradients and finally did unconstrained iterations to add the highest wavenumber details layer boundaries were implicitly defined by focus points that align along virtual marker reflector horizons each focus point sampled an area bounded by the first and last rays in the data aperture at the surface this reduced the amount of computation and the size of th

cauchy problem for a nonlinear wave equation with nonlinear damping and source terms here a b 0 and p 1 m 1 in case of ibvp in a bounded domain rn with dirichlet boundary conditions the following results are known 1 when a 0 it is proved see 1 3 8 14 16 that the solution blows up in nite time for su ciently large initial data 2 when b 0 haraux and zuazua 5 and kopackova 7 prove the global existence result for large initial data the behavior of the solution of eq 1 1 with nonlinear source and linear damping case m 1 in an abstract setting was considered by levine in 9 more precisely he showed that the solutions with negative initial energy are nonglobal

on the solvability of the cauchy characteristic problem for a nonlinear equation with iterated wave operator in the principal part we consider one multidimensional version of the cauchy characteristic problem in the light cone of the future for a hyperbolic equation with power nonlinearity with iterated wave operator in the principal part depending on the exponent of nonlinearity and spatial dimension of equation we investigate the problem on the nonexistence of global solutions of the cauchy characteristic problem the question on the local solvability of that problem is also considered

well posedness and optimal decay rates for the wave equation with nonlinear boundary damping source interaction we establish subject to some natural additional assumptions imposed on the relation between the source and the damping both well posedness and effective optimal decay rates for the solutions of a semilinear model of the wave equation the theory presented allows to consider both superlinear and sublinear behaviours of the dissipation in the presence of unstructured sources

controllability for one dimensional nonlinear wave equations with degenerate damping abstract internal exact controllability for the nonlinear wave equation in one space dimension y t t y x x g y y t h is studied where g is a nonnegative function for the case lim sup s g s ln s we obtain the global exact controllability for the equation with dirichlet boundary condition the proof is based on the combination of fixed point arguments and explicit observability estimates for the linearized wave equation with a potential that depends on both x and t for the case g s s we only get a local exact controllability by means of banach fixed point theorem

superclose and superconvergence of finite element discretizations for the stokes equations with damping a class of conforming mixed finite element methods fems are applied to the stokes equations with damping with the help of the prior estimates for the exact and approximated solutions and the appropriate choice of the parameters a n and r appeared in the problem the superclose and superconvergence results for the velocity in h 1 norm and the pressure in l 2 norm are derived to our best knowledge this is the first superconvergence analysis of conforming mixed fems for this kind nonlinear problem

parametric argument principle and its applications to cr functions and manifolds it follows from the classical argument principle that if a holomor phic mapping f from the unit discto c or more generally to c n smooth in the closed disc is homologicaly trivial on the unit circle i e h1 0 f s 1 which is equivalent to either being a point or having endpoints i e 6 then f const in other words the image of the unit disc degenerates to a point we establish a parametric version of this fact for a variety of holomorphic map pings fromto c n in place of a single mapping we find conditions for a holomorphic mapping of the unit disc depending on additional real parameters under which homological triviality of the boundary image implies collapse of the dimension of the image of the interior as an application we obtain estimates of dimensions of complex tan gent bundles of real submanifolds in c n in terms of zero moment conditions on families of closed curves covering the manifold apply ing this result to the graphs of functions we obtain solution of several known problems about characterization of holomorphic cr functions in terms of moment conditions on families of curves

blow up for nonlinear dissipative wave equations in rn abstract we consider the cauchy problem u t t u u t m 1 u t u p 1 u t x 0 r n u 0 x u 0 x u t 0 x v 0 x for 1 m p p n n 2 for n 3 we prove that for any given numbers 0 0 there exist infinitely many data u 0 v 0 in the energy space such that the initial energy e 0 the gradient norm u 0 2 and the solution of the above cauchy problem blows up in finite time

the lifespan for 3d quasilinear wave equations with nonlinear damping terms abstract in this paper we study the initial boundary value problem for a system of nonlinear wave equations involving nonlinear damping terms in a bounded domain the nonexistence of global solutions is discussed under some conditions on the given parameters estimates on the lifespan of solutions are also given our results extend and generalize the recent results in k agre m a rammaha system of nonlinear wave equations with damping and source terms differential integral equations 19 2006 1235 1270 especially the blow up of weak solutions in the case of non negative energy

global existence and global nonexistence of solutions of the cauchy problem for a nonlinearly damped wave equation abstract in this paper we consider the long time behavior of solutions of the initial value problem for semilinear wave equations of the form formula

new approach to seismic reflection event detection and velocity determination recently a number of high resolution techniques for event detection and parameter estimation velocity have emerged in the field of multichannel sonar array processing we find that a practical and computationally efficient implementation of these methods is possible for seismic reflection data this implementation results in development of the covariance measure for event detection and velocity estimation in seismic reflection data the measure is based on the eigenstructure of the sampled data covariance matrix this decomposition is carried out within hyperbolic windows that are moved through common depth point cdp data eigenvalues of the data covariance matrix allow simultaneous estimation of the noise and signal energy present within each window resulting in the development of a coherency measure computer implementation of the covariance measure provides a high resolution method for determination of velocity spectra relative to currently used techniques the method applied to synthetic data res

holomorphic extensions from open families of circles for a circle z c z c p write z w z a w a 2 0 z a p a continuous function f on extends holomorphically from into the disc bounded by if and only if the function f z z f z defined on z z z e r has a bounded holomorphic extension into a r in the paper we consider open connected families of circles c write u u e c and assume that a continuous function on u extends holomorphically from each e c we show that this happens if and only if the function f z z f z defined on z z z e u has a bounded holomorphic extension into the domain u r e q for each open family q compactly contained in c this allows us to use known facts from several complex variables in particular we use the edge of the wedge theorem to prove a theorem on real analyticity of such functions

global nonexistence for abstract evolution equations with positive initial energy abstract in this paper we consider the problem of noncontinuation of solutions of the initial value problem for abstract evolution equations of the form pu tt q t u t a t u f t u t j 0 wherepandqare linear self adjoint operators anda t u andf t u are respectively a linear operator inu typically of differential type and a nonlinear driving force our principal concern is the noncontinuation or blow up of solutions when the initial energy is positive but appropriately bounded

on nonlinear wave equations with degenerate damping and source terms in this article we focus on the global well posedness of the differential equation u tt u u k j u t u p 1 u in x 0 t where j is a sub differential of a continuous convex function j under some conditions on j and the parameters in the equations we obtain several results on the existence of global solutions uniqueness nonexistence and propagation of regularity under nominal assumptions on the parameters we establish the existence of global generalized solutions with further restrictions on the parameters we prove the existence and uniqueness of a global weak solution in addition we obtain a result on the nonexistence of global weak solutions to the equation whenever the exponent p is greater than the critical value k m and the initial energy is negative we also address the issue of propagation of regularity specifically under some restriction on the parameters we prove that solutions that correspond to any regular initial data such that u 0 h 2 h 1 0 u 1 h 1 0 are indeed strong solutions

asymptotic stability and blow up for a semilinear damped wave equation with dynamic boundary conditions abstract in this paper we consider a multi dimensional wave equation with dynamic boundary conditions related to the kelvin voigt damping global existence and asymptotic stability of solutions starting in a stable set are proved blow up for solutions of the problem with linear dynamic boundary conditions with initial data in the unstable set is also obtained

energy decay rates for the semilinear wave equation with nonlinear localized damping and source terms abstract in this paper we develop an intrinsic approach to derivation of energy decay rates for the semilinear wave equation with localized interior nonlinear monotone damping g u t and a source term f u the proposed approach allows to consider in an unified way much more general classes of hyperbolic problems than addressed before in the literature these generalizations refer to both geometric and topological aspects of the problem the method leads to optimal decay rates for solutions of semilinear hyperbolic equations driven by a source of critical exponent and subjected to a nonlinear damping localized in a small region adjacent to a portion of the boundary the distinct features of the model include i neumann boundary conditions are assumed and ii no growth conditions are imposed on the damping g s it is well known that neumann boundary does not satisfy lopatinski condition and therefore the analysis of propagation of energy in the absence of the damping on the neumann part of the boundary requires special geometric considerations in addition the sole conditions assumed on g s are monotonicity continuity and g 0 0 in particular no differentiability and no growth conditions are imposed on the damping both at the origin and at the infinity the asymptotic decay rates for the energy function are obtained from an intrinsic algorithm driven by solutions of simple ode several examples illustrate the theory by exhibiting various decay rates exponential algebraic rational logarithmic etc for the energy functional an important corollary of our energy decay theorem is a stability result which shows that under certain conditions when dissipation is sublinear at infinity the solution of the system remains uniformly bounded for all time in the norms above the finite energy level even in the presence of a nonlinear source term

strichartz estimates in the hyperbolic space and global existence for the semilinear wave equation the aim of this article is twofold first we consider the wave equation in the hyperbolic space hi and obtain the counterparts of the strichartz type estimates in this context next we examine the relationship between semilinear hyperbolic equations in the minkowski space and in the hyperbolic space this leads to a simple proof of the recent result of georgiev lindblad and sogge on global existence for solutions to semilinear hyperbolic problems with small data shifting the space time strichartz estimates from the hyperbolic space to the minkowski space yields weighted strichartz estimates in rn x 1r which extend the ones of georgiev lindblad and sogge

two grid mfeas for the incompressible stokes type variational inequality with damping abstract in this paper we study two grid mixed finite element algorithms mfeas for the stationary incompressible stokes equations with damping and nonlinear slip boundary conditions we set up the weak formulation and obtain the well posedness then employing the mixed finite element method some optimal error estimates between the exact solution and the approximation solution are derived two kinds of two grid mfeas based on the stokes correction and newton type correction are established some error estimates for two grid mfeas are obtained several numerical results are presented to confirm our theoretical findings

high resolution bootstrapped differential semblance abstractwe formulated two coherency measures based on the bootstrapped differential semblance bds estimator that offered higher resolution in parameter tracking than did standard normalized differential semblance bootstrapping is a statistical resampling procedure used to infer estimates of standard errors and confidence intervals from data samples for which the statistical properties are unattainable via simple means or when the probability density function is unkown or difficult to estimate the first proposed estimator was based on a deterministic sorting of original offset traces by alternating near and far offsets to achieve maximized time shifts between adjacent traces the near offsets were indexed with odd integers while the even integers were used to index far offsets that were located at a constant index increment from the previous trace the second was the product of several bds terms with the first term being the deterministic bds defined above the other terms were generated by random

global nonexistence theorems for a class of evolution equations with dissipation we study abstract evolution equations with nonlinear damping terms and source terms including as a particular case a nonlinear wave equation of the type ba cl u tt delta u b u t m 2 u t c u p 2 u t x in 0 t times omega 6pt u t x 0 t x in 0 t times partial omega 6pt u 0 cdot u 0 in h 0 1 omega quad u t 0 cdot v 0 in l 2 omega es ea where 0 p 2 m 1 we prove a global nonexistence theorem for positive initial value of the energy when 1 1

blow up for semilinear wave equation with boundary damping and source terms abstract in this paper we consider the semilinear wave equation with boundary damping and source terms this work is devoted to prove a finite time blow up result under suitable condition on the initial data and positive initial energy

a mixed fem for navier stokes type variational inequality with nonlinear damping term abstract in this work we consider a mixed finite element method fem for incompressible navier stokes equations with nonlinear damping term and friction boundary conditions after establishing the variational formulation we show the well posedness of this problem subsequently we focus our attention on the mixed fem and analyze the galerkin approximation to this system then some optimal error estimates are deduced in the end some iterative algorithms are presented and numerical results are given to verify the theoretical analysis

optimality of high resolution array processing using the eigensystem approach in the classical approach to underwater passive listening the medium is sampled in a convenient number of look directions from which the signals are estimated in order to build an image of the noise field in contrast a modern trend is to consider the noise field as a global entity depending on few parameters to be estimated simultaneously in a gaussian context it is worthwhile to consider the application of likelihood methods in order to derive a detection test for the number of sources and estimators for their locations and spectral levels this paper aims to compute such estimators when the wavefront shapes are not assumed known a priori this justifies results previously found using the asymptotical properties of the eigenvalue eigenvector decomposition of the estimated spectral density matrix of the sensor signals they have led to a variety of high resolution array processing methods more specifically a covariance matrix test for equality of the smallest eigenvalues is presented for source detection for source localization a best fit method and a test of orthogonality between the smallest eigenvectors and the source vectors are discussed

testing analyticity on rotation invariant families of curves let r c c be a piecewise smooth jordan curve symmetric with respect to the real axis which contains the origin in its interior and which is not a circle centered at the origin let q be the annulus obtained by rotating r around the origin we characterize the curves r with the property that if f e c q is analytic on sr for every 181 1 then f is analytic in int q

zero integrals on circles and characterizations of harmonic and analytic functions we determine the kernels of two circular radon transforms of continuous functions on an annulus and use this to obtain a characterization of harmonic functions in the open unit disc which involves poisson averages over circles computed at only one point of the disc and to obtain a version of morera s theorem which involves only the circles which surround the origin

on wave equations of the p laplacian type with supercritical nonlinearities abstract this article focuses on a quasilinear wave equation of p laplacian type u t t p u u t f u in a bounded domain r 3 with a sufficiently smooth boundary subject to a generalized robin boundary condition featuring boundary damping and a nonlinear source term the operator p 2 p 3 denotes the classical p laplacian the interior and boundary terms f u h u are sources that are allowed to have a supercritical exponent in the sense that their associated nemytskii operators are not locally lipschitz from w 1 p into l 2 or l 2 under suitable assumptions on the parameters we provide a rigorous proof of existence of a local weak solution which can be extended globally in time provided the damping terms dominate the corresponding sources in an appropriate sense moreover a blow up result is proved for solutions with negative initial total energy

global existence and blow up of solutions for a system of nonlinear viscoelastic wave equations with damping and source abstract in this paper we investigate the global existence and finite time blow up of solutions to the system of nonlinear viscoelastic wave equations u t t u 0 t g 1 t u d u t m 1 u t f 1 u v v t t v 0 t g 2 t v d v t r 1 v t f 2 u v in 0 t with initial and dirichlet boundary conditions where is a bounded domain in r n n 1 2 3 under suitable assumptions on the functions g i f i i 1 2 the initial data and the parameters in the equations we establish several results concerning local existence global existence uniqueness and finite time blow up property

the first darboux problem for wave equations with a nonlinear positive source term abstract we consider the first darboux problem for nonlinear wave equations with positive power nonlinearity source term depending on the power of nonlinearity we investigate the problem on a global existence and blow up of solutions of the first darboux problem the question of local solvability of the problem is also considered

on existence and nonexistence of global solutions of cauchy goursat problem for nonlinear wave equations abstract we consider the cauchy goursat initial characteristic problem for nonlinear wave equations with power nonlinearity depending on the power of nonlinearity and the parameter in an equation we investigate the problem on existence and nonexistence of global solutions of the cauchy goursat problem the question on local solvability of the problem is also considered

high resolution velocity spectra using eigenstructure methods stacking spectra provide maximum likelihood estimates for the stacking velocity or for the ray parameter of well separated reflections in additive white noise however the resolution of stacking spectra is limited by the aperture of the array and the frequency of the data despite these limitations parametric spectral estimation methods achieve better resolution than does stacking to improve resolution the parametric methods introduce a parsimonious model for the spectrum of the data in particular when the data are modeled as the superposition of wavefronts the properties of the eigenstructure of the data covariance matrix can be used to obtain high resolution spectra the traditional stacking spectra can also be expressed as a function of the data covariance matrix and directly compared to the eigenstructure spectra the superiority of the latter in separating closely interfering reflections is then apparent from a simple geometric interpretation eigenstructure methods were originally developed