exponential energy decay estimate for the solutions of internally damped wave equation in a bounded domain abstract here we are concerned about the stability of the solution of internally damped wave equation y y y with small damping constant 0 in a bounded domain in r n under mixed undamped boundary conditions a uniform exponential energy decay rate e t me t e 0 where m 1 and 0 0 being a quadratic function of is proved for the solution of this type of boundary value problem earlier authors have considered the undamped wave equation with certain forms of damped boundary conditions proving similar and faster energy decay rates

backstepping boundary control of a wave pde with spatially distributed time invariant unknown disturbances an observer based boundary control scheme is suggested for an infinite dimensional system modeled as a wave partial differential equation pde with in domain and boundary disturbances we consider a collocated case where the sensors and the actuators are located at the same boundary the aim of the controller is to regulate the rate of change of the opposite boundary around a given reference the unknown in domain disturbance is spatially distributed but it is constant in time same as the unknown boundary disturbance the problem is reformulated as a stabilization of an linear time invariant lti system with simultaneous delays in input and output channels the exponential stability of the equilibrium of the closed loop system is proven the performance of the controller is shown using numerical simulations

eigenvalue approximation by mixed and hybrid methods note univ maryland dept math college pk md 20742 ecole polytech ctr math appl f 91128 palaiseau france univ paris 6 f 75230 paris 05 france mercier b cea limeil f 94190 villeneuve france isi document delivery no lq584times cited 29cited reference count 44 reference asn article 1981 005doi 10 2307 2007651 record created on 2006 08 24 modified on 2017 05 12

regularized solutions for abstract volterra equations abstract we introduce a two kernel dependent family of strong continuous operators defined in a banach space which allows us to consider in an unified treatment the notions of among others c 0 semigroups of operators cosine families n times integrated semigroups resolvent families and k generalized solutions the results are applied to the study of existence and uniqueness of solutions for the volterra equation of convolution type u f a au in the case a is not necessarily densely defined examples for equations defined in l p spaces are also given

existence results for fractional order semilinear functional differential equations with nondense domain abstract in this paper we establish sufficient conditions for existence and uniqueness of solutions for some nondensely defined semilinear functional differential equations involving the riemann liouville derivative our approach is based on integrated semigroup theory the banach contraction principle and the nonlinear alternative of leray schauder type

on a solution to fractional order integrodifferential equations with analytic semigroups abstract in this paper we study a class of fractional order integrodifferential equations considered in an arbitrary banach space using the theory of analytic semigroups we establish the existence uniqueness and regularity of a mild solution to these fractional order integrodifferential equations

characterization of compactness for resolvents and its applications abstract in this paper we derive some characterizations of compactness for resolvents as well as the subordination principle associated with the compactness as applications we obtain the existence of fractional evolution equations by using schauder s fixed point theorem a simple example about fractional heat equation is also given to illustrate our theory

boundary stabilization of nonlinear vibrations of a flexible structure in a bounded domain in rn abstract we study a problem of boundary stabilization of the vibrations of elastic structure governed by the nonlinear integro differential equation u a 2 b u 2 d x u f in a bounded domain in r n with a smooth boundary under mixed boundary conditions to stabilize this system we apply a velocity feedback control only on a part of the boundary we prove that the solution of such system is stable subject to some restriction on the uncertain disturbing force f we also estimate the total energy of the system over any time interval 0 t with a tolerance level of the disturbances finally we establish the uniform decay of solution by a direct method with an explicit form of exponential energy decay estimate when this disturbing force f is insignificant

existence of asymptotically almost periodic solutions for damped wave equations abstract in this paper a class of nonlinear damped wave equations of the form u t u t a u t a u t f t u t t 0 satisfying with prescribed initial conditions are studied some sufficient conditions are established for the existence and uniqueness of an asymptotically almost periodic solution these results have significance in the study of vibrations of flexible structures possessing internal material damping finally an example is presented to illustrate the feasibility and effectiveness of the results

existence of the mild solution for fractional semilinear initial value problems abstract in this paper we will study the existence and uniqueness of mild solution for the semilinear initial value problem of non integer order u t a u t f t u t g u t s u t where 0 1 and f t u t g u t s u t is a given function

bounded input bounded output stability of a damped nonlinear string in this paper we prove that the displacement of a damped nonlinear string under bounded distributed forces is bounded the proof is achieved by showing that an energy like lyapunov function corresponding to the string is bounded

global smooth solutions for the quasilinear wave equation with boundary dissipation abstract we consider the existence of global solutions of the quasilinear wave equation with a boundary dissipation structure of an input output in high dimensions when initial data and boundary inputs are near a given equilibrium of the system our main tool is the geometrical analysis the main interest is to study the effect of the boundary dissipation structure on solutions of the quasilinear system we show that the existence of global solutions depends not only on this dissipation structure but also on a riemannian metric given by the coefficients and the equilibrium of the system some geometrical conditions on this riemannian metric are presented to guarantee the existence of global solutions in particular we prove that the norm of the state of the system decays exponentially if the input stops after a finite time which implies the exponential stabilization of the system by boundary feedback

on recent developments in the theory of abstract differential equations with fractional derivatives abstract this note is motivated from some recent papers treating the problem of the existence of a solution for abstract differential equations with fractional derivatives we show that the existence results in agarwal et al 2009 1 belmekki and benchohra 2010 2 darwish et al 2009 3 hu et al 2009 4 mophou and n guerekata 2009 6 7 mophou 2010 8 9 muslim 2009 10 pandey et al 2009 11 rashid and el qaderi 2009 12 and tai and wang 2009 13 are incorrect since the considered variation of constant formulas is not appropriate in this note we also consider a different approach to treat a general class of abstract fractional differential equations

the resolution property for schemes and stacks we prove the equivalence of two fundamental properties of algebraic stacks being a quotient stack in a strong sense and the resolution property which says that every coherent sheaf is a quotient of some vector bundle moreover we prove these properties in the important special case of orbifolds whose associated algebraic space is a scheme mathematics subject classification primary 14a20 secondary 14l30

a note on the boundary stabilization of the wave equation we study the energy decay rates of the wave equation in a domain where boundary damping is present we generalize the geometrical conditions obtained earlier in j math purer appl 58 1979 pp 249 273 by using some more general multipliers of strauss comm pure appl math 28 1975 pp 265 278 the interaction between distributed damping and boundary damping is discussed a regulator problem is also formally discussed by the synthesis method

exact controllability stabilization and perturbations for distributed systems exact controllability is studied for distributed systems of hyperbolic type or for petrowsky systems like plate equations the control is a boundary control or a local distributed control exact controllability consists in trying to drive the system to rest in a given finite time the solution of the problems depends on the function spaces where the initial data are taken and also depends on the function space where the control can be chosen a systematic method named hum for hilbert uniqueness method is introduced as the terminology indicates it is based on uniqueness results classical or new and on hilbert spaces constructed in infinitely many ways by using uniqueness a number of applications are indicated having a general method for exact controllability implies having a general method for stabilization this leads to new and complicated nonlinear riccati s type pdes to be compared with direct methods when available in the last part of the paper we consider how all this behaves fo

existence and uniqueness of mild solutions to impulsive fractional differential equations this paper is concerned with the existence and uniqueness of a mild solution to impulsive fractional semilinear differential equations the results are obtained by means of fixed point methods we also give an example of such problems

borel moore homology riemann roch transformations and local terms abstract we develop various properties of etale borel moore homology and study its relationship with intersection theory using gabber s localized cycle classes we define etale homological gysin morphisms and show that they are compatible with the cycle class map and gysin morphisms in intersection theory we also study etale versions of bivariant operations and establish their compatibility with riemann roch transformations and fulton macpherson bivariant operations as an application of these techniques we show that in certain situations local terms for correspondences acting on etale cohomology are given by cycle classes

the approximation of the maxwell eigenvalue problem using a least squares method in this paper we consider an approximation to the maxwell s eigenvalue problem based on a very weak formulation of two div curl systems with complementary boundary conditions we formulate each of these div curl systems as a general variational problem with different test and trial spaces i e the solution space is l 2 l 2 3 and components in the test spaces are in subspaces of h 1 the sobolev space of order one on the computational domain q a finite element least squares approximation to these variational problems is used as a basis for the approximation using the structure of the continuous eigenvalue problem a discrete approximation to the eigenvalues is set up involving only the approximation to either of the div curl systems we give some theorems that guarantee the convergence of the eigenvalues to those of the continuous problem without the occurrence of spurious values finally some results of numerical experiments are given

computation of maxwell singular solution by nodal continuous elements abstract in this paper we propose and analyze a nodal continuous and h 1 conforming finite element method for the numerical computation of maxwell s equations with singular solution in a fractional order sobolev space h r where r may take any value in the most interesting interval 0 1 the key feature of the method is that mass lumping linear finite element l 2 projections act on the curl and divergence partial differential operators so that the singular solution can be sought in a setting of l 2 space we shall use the nodal continuous linear finite elements enriched with one element bubble in each element to approximate the singular and non h 1 solution discontinuous and nonhomogeneous media are allowed in the method some error estimates are given and a number of numerical experiments for source problems as well as eigenvalue problems are presented to illustrate the superior performance of the proposed method

abstract fractional cauchy problems with almost sectorial operators abstract of concern are the cauchy problems for linear and semilinear time fractional evolution equations involving in the linear part a linear operator a whose resolvent satisfies the estimate of growth 1 0 in a sector of the complex plane which occurs when one considers for instance the partial differential operators in the limit domain of dumb bell with a thin handle or in the space of holder continuous functions by constructing a pair of families of operators in terms of the generalized mittag leffler type functions and the resolvent operators associated with a for the first time and a deep analysis on the properties for these families we obtain the existence and uniqueness of mild solutions and classical solutions to the cauchy problems moreover we present three examples to illustrate the feasibility of our results

polygonal spline spaces and the numerical solution of the poisson equation it is known that generalized barycentric coordinates can be used to form bernstein polynomial like functions over a polygon with any number of sides we propose to use these functions to form a space of continuous polygonal splines piecewise defined functions of order d over a partition consisting of polygons which is able to reproduce all polynomials of degree d locally supported basis functions for the space are constructed for order d ge 2 the construction for d 2 is simpler than the serendipity quadratic finite elements that have appeared in the recent literature the number of basis functions is similar to but fewer than those of the virtual element method we use them for the numerical solution of the poisson equation on two special types of nontriangular partitions to present a proof of concept for solving pdes over polygonal partitions numerical solutions based on quadrangulations and pentagonal partitions are demonstrated to show the efficiency of these polygonal spline functions

a mixed h 1 conforming finite element method for solving maxwell s equations with non h 1 solution in this paper we propose and analyze a mixed h 1 conforming finite element method for solving maxwell s equations in terms of electric field and lagrange multiplier where the multiplier is intr

frobenius semisimplicity for convolution morphisms this article concerns properties of mixed ell adic complexes on varieties over finite fields related to the action of the frobenius automorphism we establish a fiberwise criterion for the semisimplicity and frobenius semisimplicity of the direct image complex under a proper morphism of varieties over a finite field we conjecture that the direct image of the intersection complex on the domain is always semisimple and frobenius semisimple this conjecture would imply that a strong form of the decomposition theorem of beilinson bernstein deligne gabber is valid over finite fields we prove our conjecture for generalized convolution morphisms associated with partial affine flag varieties for split connected reductive groups over finite fields as a crucial tool we develop a new schematic theory of big cells for loop groups with suitable reformulations the main results are valid over any algebraically closed ground field

the characteristic class and ramification of an l adic etale sheaf we introduce the characteristic class of an l adic etale sheaf using a cohomological pairing due to verdier sga5 as a consequence of the lefschetz verdier trace formula its trace computes the euler poincare characteristic of the sheaf we compare the characteristic class to two other invariants arising from ramification theory one is the swan class of kato saito 17 and the other is the 0 cycle class defined by kato for rank 1 sheaves in 16

note on boundary stabilization of wave equations an energy decay rate is obtained for solutions of wave type equations in a bounded region in mathbb r n whose boundary consists partly of a nontrapping reflecting surface and partly of an energy absorbing surface unlike most previous results on this subject the results presented here are potentially valid for regions having connected boundaries

stabilization of quasi linear vibrations of an inhomogeneous beam in this note we study the stabilization of a vibrating inhomogeneous beam under distributed disturbing force we prove that the amplitude of such vibration is bounded subject to some restriction on the uncertain disturbing force we also estimate the total energy of the system over time interval 0 t for any time t 0 together with a tolerance level of the disturbance finally we establish the uniform decay of solution with an explicit form of exponential energy decay estimate when the uncertain disturbances are insignificant

semilinear fractional integro differential equations with compact semigroup abstract in this paper we study the local and global existence of mild solutions to a class of fractional integro differential equations in an arbitrary banach space associated with operators generating compact semigroup on the banach space

weighted regularization of maxwell equations in polyhedral domains we present a new method of regularizing time harmonic maxwell equations by a bf grad div term adapted to the geometry of the domain this method applies to polygonal domains in two dimensions as well as to polyhedral domains in three dimensions in the presence of reentrant corners or edges the usual regularization is known to produce wrong solutions due the non density of smooth fields in the variational space we get rid of this undesirable effect by the introduction of special weights inside the divergence integral standard finite elements can then be used for the approximation of the solution this method proves to be numerically efficient

l p maximal regularity for second order cauchy problems we introduce the concept of l p maximal regularity for second order cauchy problems we prove l p maximal regularity for an abstract model problem and we apply the abstract results to prove existence uniqueness and regularity of solutions for nonlinear wave equations

ramification theory for varieties over a perfect field for an l adic sheaf on a variety of arbitrary dimension over a perfect field we define the swan class measuring the wild ramification as a 0 cycle class supported on the ramification locus we prove a lefschetz trace formula for open varieties and a generalization of the grothendieck ogg shararevich formula using the swan class

new mixed elements for maxwell equations new inf sup stable mixed elements are proposed and analyzed for solving the maxwell equations in terms of electric field and lagrange multiplier nodal continuous lagrange elements of any order on simplexes in two and three dimensional spaces can be used for the electric field the multiplier is compatibly approximated always by the discontinuous piecewise constant elements a general theory of stability and error estimates is developed when applied to the eigenvalue problem we show that the proposed mixed elements provide spectral correct spurious free approximations essentially optimal error bounds only up to an arbitrarily small constant are obtained for eigenvalues and for both singular and smooth solutions numerical experiments are performed to illustrate the theoretical results

a family of optimal lagrange elements for maxwell s equations abstract in this paper we propose and study a new lagrange finite element method for the two dimensional maxwell s equations its solution may be singular because of the nonsmooth domain with reentrant corners the proposed method allows the standard lagrange elements on barycentric refinements of any order greater than or equal to two we analyze the proposed method for the eigenvalue problem and the indefinite source problem obtaining the well posedness and optimal error estimates numerical results are presented for confirming the theoretical results

a uniformly stable fortin operator for the taylor hood element we construct a new fortin operator for the lowest order taylor hood element which is uniformly stable both in l 2 and h 1 the construction which is restricted to two space dimensions is based on a tight connection between a subspace of the taylor hood velocity space and the lowest order nedelec edge element general shape regular triangulations are allowed for the h 1 stability while some mesh restrictions are imposed to obtain the l 2 stability as a consequence of this construction a uniform inf sup condition associated the corresponding discretizations of a parameter dependent stokes problem is obtained and we are able to verify uniform bounds for a family of preconditioners for such problems without relying on any extra regularity ensured by convexity of the domain

a new approximation technique for div curl systems in this paper we describe an approximation technique for div curl systems based in l where is a domain in 3 we formulate this problem as a general variational problem with different test and trial spaces the analysis requires the verification of an appropriate inf sup condition this results is a very weak formulation where the solution space is l and the data reside in various negative norm spaces subsequently we consider finite element approximations based on this weak formulation the main approach of this paper involves the development of stable pairs of discrete test and trial spaces with this approach we enlarge the test space so that the discrete inf sup condition holds and use a negative norm least squares formulation to reduce to a uniquely solvable linear system this leads to optimal order estimates for problems with minimal regularity which is important since it is possible to construct magnetostatic field problems whose solutions have low sobolev regularity e g h with 0 s 1 2 the resulting algebraic equations are symmetric positive definite and well conditioned a second approach using a smaller test space which adds terms to the form for stabilization will also be mentioned some numerical results are also presented