solvability of linear local and nonlocal robin problems over c ω abstract let r n be a bounded lipschitz domain we first consider an elliptic boundary value problem with general robin boundary conditions the boundary conditions can be either local or nonlocal depending on the conditions imposed on the elliptic operator we prove that this boundary value problem is uniquely solvable and moreover we show that such weak solution is holder continuous on we also prove that a realization of the associated differential operator with generalized local or nonlocal robin boundary conditions generates an analytic c 0 semigroup of angle 2 over c we conclude by applying the elliptic regularity theory to solve the corresponding cauchy problem over c

translation representations for automorphic solutions of the wave equation in non euclidean spaces i this paper deals with the spectral theory of the laplace beltrami operator acting on automorphic functions in n dimensional hyperbolic space hn we study discrete subgroups which have a fundamental polyhedron f with a finite number of sides and infinite volume concerning these we have shown previously that the spectrum of contains at most a finite number of point eigenvalues in 1 2 n 1 2 0 and none less than 1 2 n 1 2 here we prove that the spectrum of is absolutely continuous and of infinite multiplicity in 1 2 n 1 2 our approach uses the non euclidean wave equation introduced by faddeev and pavlov energy ef is defined as ut ut u lu where the bracket is the l2 scalar product over a fundamental polyhedron with respect to the invariant volume of the hyperbolic metric energy is conserved under the group of operator u t relating initial data to data at time t we construct two isometric representations of the space of automorphic data by l2 r n which transmute the action of u t into translation these representations are given explicitly in terms of integrals of the data over horospheres in part ii we shall show the completeness of these representations utt lu 0 l 1 2 n 1 2

on a class of nonlinear dispersive dissipative interactions abstract we study a prototype dissipative dispersive equation ut a um x un xxx uk xx a consts which represents a wide variety of interactions at the critical value k m n 2 which separates dispersive and dissipation dominated phenomena these effects are in a detailed balance and the patterns formed do not depend on the amplitude in particular when m n 2 k 1 the equation can be transformed into a form free of convection and dissipation making it accessible to analysis both bounded and unbounded oscillations as well as solitary waves are found a variety of exact solutions are presented with a notable example being a solitary doublet for n 1 and a 2 3 2 the problem may be mapped into a linear equation leading to rational periodic or aperiodic solutions among others

existence of solutions to quasi linear elliptic problems with generalized robin boundary conditions abstract we characterize the l q solvability of a class of quasi linear elliptic equations involving the p laplace operator with generalized nonlinear robin type boundary conditions on bad domains some uniqueness results are also given

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

the tanh method for a reliable treatment of the k n n and the kp n n equations and its variants abstract in this work the nonlinear k n n and kp n n equations and its variants are analytically studied we show that these equations may exhibit compactons solitons or periodic solutions by using the tanh method the analysis reveals the change of the physical structure of the solutions as a result of the exponents and the coefficients of the derivatives

dirichlet and neumann boundary conditions for the p laplace operator what is in between let p 1 and let r n be a bounded domain with lipschitz continuous boundary we characterize all order preserving semigroups on l 2 which are generated by convex lower semicontinuous local functionals and which are sandwiched between the semigroups generated by the p laplace operator with dirichlet and neumann boundary conditions we show that every such semigroup is generated by the p laplace operator with robin type boundary conditions

tri hamiltonian duality between solitons and solitary wave solutions having compact support a simple scaling argument shows that most integrable evolutionary systems which are known to admit a bi hamiltonian structure are in fact governed by a compatible trio of hamiltonian structures we demonstrate how their recombination leads to integrable hierarchies endowed with nonlinear dispersion that supports compactons solitary wave solutions having compact support or cusped and or peaked solitons a general algorithm for effecting this duality between classical solitons and their nonsmooth counterparts is illustrated by the construction of dual versions of the modified korteweg de vries equation the nonlinear schr odinger equation the integrable boussinesq system used to model the two way propagation of shallow water waves and the ito system of coupled nonlinear wave equations these hierarchies include a remarkable variety of interesting integrable nonlinear differential equations textcopyright 1996 the american physical society

novel modal methods for transient analysis with a reduced order model based on enhanced craig bampton formulation abstract for transient analysis of structural dynamics with reduced order model rom data recovery procedures that use modal methods such as the classical mode acceleration ma and modal displacement md methods are an important step in order to increase the convergence and accuracy of the solution in this work we propose novel ma and md methods for highly accurate transient analysis with a reduced order model based on enhanced craig bampton ecb formulation which is an extension of the classical craig bampton cb method that is a way to reduce the size of a finite element fe model the performance of the proposed data recovery approach is demonstrated with two numerical examples we also investigate the relation between the proposed and classical ma and md methods

the sine cosine and the tanh methods reliable tools for analytic treatment of nonlinear dispersive equations the sine cosine method and the tanh method are used for analytic treatment of nonlinear dispersive equations nonlinear variants of boussinesq equation are used as vehicles to show the strength of these methods solutions of distinct physical structures solitons compactons solitary patterns solutions and periodic solutions are formally derived the results show that the change in physical structures of the obtained solutions depends mainly on exponents and on the coefficients of the derivatives involved

traveling wave solutions of the generalized nonlinear evolution equations solitary wave solutions for a family of nonlinear evolution equations with an arbitrary parameter in the exponents are constructed some of the obtained solutions seem to be new

construction of new solutions to the fully nonlinear generalized camassa holm equations by an indirect f function method an indirect f function method is introduced to solve the generalized camassa holm equation with fully nonlinear dispersion and fully nonlinear convection c l n p taking advantage of elliptic equation this f function is used to map the solutions of the generalized camassa holm equation to those of the elliptic equation as a result we can successfully obtain in a unified way and for special values of the parameters of this equation many exact solutions expressed by various single and combined nondegenerative jacobi elliptic function solutions and their degenerative solutions soliton combined soliton solutions and triangular solutions as the modulus m is driven to 1 and 0

domain wall solutions of kdv like equations with higher order nonlinearity the author considers certain nonlinear partial differential equations which are korteweg de vries kdv like equations with higher order nonlinearity it is shown that these have kink domain wall solutions for particular values of the coefficients of the nonlinear terms the solutions are compared with the standard known solution of the lambda phi 2n field theories some conservation laws for these systems of equations are also given

an algebraic method for finding a series of exact solutions to integrable and nonintegrable nonlinear evolution equations an algebraic method is devised to uniformly construct a series of exact solutions for general integrable and nonintegrable nonlinear evolution equations compared with most existing tanh methods the jacobi function expansion method or other sophisticated methods the proposed method not only gives new and more general solutions but also provides a guideline to classify the various types of the solutions according to the values of some parameters the solutions obtained in this paper include a polynomial solutions b exponential solutions c rational solutions d triangular periodic wave solutions e hyperbolic and solitary wave solutions and f jacobi and weierstrass doubly periodic wave solutions the efficiency of the method can be demonstrated on a large variety of nonlinear equations such as those considered in this paper new 2 1 dimensional calogero kdv equation 3 1 dimensional jimbo miwa equation symmetric regular long wave equation drinfel d sokolov wilson equation 2 1 dimensional generalized dispersive long wave equation double sine gordon equation calogero degasperis fokas equation and coupled schrodinger boussinesq equation in addition the links among our proposed method the tanh method the extended method and the jacobi function expansion method are also clarified generally

morera theorems for complex manifolds abstract we prove morera theorems for the radon transform integrating on geodesic spheres on complex analytic manifolds of arbitrary dimension to avoid pathologies we assume that the radius of each sphere of integration is less than the injectivity radius at its center the proofs of the main results are local and they involve the microlocal properties of associated radon transforms and a theorem of hormander kawai and kashiwara on microlocal singularities we consider morera theorems for spheres of fixed radius and spheres of arbitrary radius

new peakon solitary wave and periodic wave solutions for the modified camassa holm equation abstract in this paper an independent variable transformation is introduced to solve the modified camassa holm equation using the bifurcation theory and the method of phase portrait analysis some peakons solitary waves and periodic waves are found and their exact parametric representations in explicit form and in implicit form are obtained

a simple approach for reducing the order of equations with higher order nonlinearity abstract in this paper we introduce a simple approach to reduce the order of equations with higher order nonlinearity we choose the generalized forms of the kdv equation the camassa holm equation and the zakharov kuznetsov equation to illustrate the validity and advantages of the approach then the explicit solutions with different physical structures of the reduced equations can be discussed further the approach used here can be applied to some other nonlinear equations with higher order nonlinearity and is also suitable for some higher dimensional models

the camassa holm kp equations with compact and noncompact travelling wave solutions abstract in this paper two variants of camassa holm kp equations are investigated compactons solitons with the absence of infinite tails solitons nonlinear localized waves of infinite support solitary patterns having infinite slopes or cusps and plane periodic solutions are formally derived the work highlights the qualitative change in the physical structures of the obtained solutions

travelling wave solutions of generalized forms of burgers burgers kdv and burgers huxley equations in this work exact travelling wave solutions of generalized forms of burgers burgers kdv and burgers huxley equations are obtained the analysis rests mainly on the standard tanh method the work emphasizes the need for a transformation formula for the case where the parameter m is non integer the approach can be used in a variety of many types of nonlinearity

exact travelling wave solutions for a generalized zakharov kuznetsov equation in this paper by means of a proper transformation and symbolic computation we study the exact travelling wave solutions for a generalized zakharov kuznetsov gzk equation by using the extended tanh method and direct assumption method as a result rich exact travelling wave solutions which contain new kink shaped solitons bell shaped solitons periodic solutions combined formal solitons rational solutions and singular solitons for gzk equation are obtained

orbital stability of peakons for the degasperis procesi equation with strong dispersion abstract in this paper we study the orbital stability of the peakons for the degasperis procesi equation with a strong dispersive term on the line using the method in z lin y liu stability of peakons for the degasperis procesi equation comm pure appl math 62 2009 125 146 we prove that the shapes of these peakons are stable under small perturbations some previous results are extended

incoming and outgoing waves on etudie des espaces de solutions de l equation d onde u tt lu 0 ou lf f xx qf qui apparait dans la theorie de la diffusion de lax phillips

the laplace operator on a hyperbolic manifold i spectral and scattering theory using techniques of stationary scattering theory for the schrodinger equation we show absence of singular spectrum and obtain incoming and outgoing spectral representations for the laplace beltrami operator on manifolds mn arising as the quotient of hyperbolic n dimensional space by a geometrically finite discrete group of hyperbolic isometries we consider manifolds mn of infinite volume in subsequent papers we will use the techniques developed here to analytically continue eisenstein series for a large class of discrete groups including some groups with parabolic elements

regularized perimeter for topology optimization the perimeter functional is known to oppose serious difficulties when it has to be handled within a topology optimization procedure in this paper a regularized perimeter functional mbox per varepsilon defined for two and three dimensional domains is introduced on one hand the convergence of mbox per varepsilon to the exact perimeter when varepsilon tends to zero is proved on the other hand the topological differentiability of mbox per varepsilon for varepsilon 0 is analyzed these features lead to the design of a topology optimization algorithm suitable for perimeter dependent objective functionals several numerical results illustrate the method

on exact travelling wave solutions for two types of nonlinear k n n equations and a generalized kp equation in this paper we study two types of genuinely nonlinear k n n equations and a generalized kp equation by developing a mathematical method based on the reduction of order of nonlinear differential equations we derive general formulas for the travelling wave solutions of the three equations the compactons solitary patterns solitons and periodic solutions obtained are expressed analytically it is shown that the y and z components of the wave number vectors in the travelling wave solutions of the generalized kp equation remain free and arbitrary constants the work generalizes the known results of travelling wave solutions for the three equations

a class of quasi linear parabolic and elliptic equations with nonlocal robin boundary conditions abstract let p 1 n r n a bounded w 1 p extension domain and let be an upper d ahlfors measure on with d n p n we show in the first part that for every p 2 n n 2 n 1 n a realization of the p laplace operator with nonlinear generalized nonlocal robin boundary conditions generates a nonlinear strongly continuous submarkovian semigroup on l 2 and hence the associated first order cauchy problem is well posed on l q for every q 1 in the second part we investigate existence uniqueness and regularity of weak solutions to the associated quasi linear elliptic equation more precisely global a priori estimates of weak solutions are obtained

nonlinear stochastic partial differential equations with singular diffusivity and gradient stratonovich noise abstract we study existence and uniqueness of a variational solution in terms of stochastic variational inequalities svi to stochastic nonlinear diffusion equations with a highly singular diffusivity term and multiplicative stratonovich gradient type noise we derive a commutator relation for the unbounded noise coefficients in terms of a geometric killing vector condition the drift term is given by the total variation flow respectively by a singular p laplace type operator we impose nonlinear zero neumann boundary conditions and precisely investigate their connection with the coefficient fields of the noise this solves an open problem posed in barbu et al 2013 7 and barbu and rockner 2015 10

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

the heat equation with nonlinear generalized robin boundary conditions abstract let r n be a bounded domain and let be an admissible measure on we show in the first part that if has the h 1 extension property then a realization of the laplace operator with generalized nonlinear robin boundary conditions formally given by u d x u d 0 on generates a strongly continuous nonlinear submarkovian semigroup s b s b t t 0 on l 2 we also obtain that this semigroup is ultracontractive in the sense that for every u v l p p 2 and every t 0 one has s b t u s b t v c 1 e c 2 t t n 2 p u v p for some constants c 1 c 2 0 in the second part we prove that if is a bounded lipschitz domain one can also define a realization of the laplacian with nonlinear robin boundary conditions on c and this operator generates a strongly continuous and contractive nonlinear semigroup