weighted pseudo almost periodic mild solutions of semilinear evolution equations with nonlocal conditions in this paper applying the theory of semigroups of operators to evolution families and banach fixed point theorem we prove the existence and uniqueness of the weighted pseudo almost periodic mild solution of the semilinear evolution equation x t a t x t f t x t with nonlocal conditions x 0 x 0 g x in banach space x under some suitable hypotheses

an optimal control approach to the optical flow problem abstract the optical flow problem is reduced to an optimal control problem governed by a linear parabolic equation having the unknown velocity field the optical flow as drift term this model is derived from a new assumption that is the brightness intensity is conserved on a moving pattern driven by a gaussian stochastic process the optimality conditions are deduced by a passage to the limit technique in an approximating optimal control problem introduced for a regularization purpose finally the controller uniqueness is addressed

weighted pseudo almost periodic solutions of a class of abstract differential equations abstract for abstract linear functional differential equations with a weighted pseudo almost periodic forcing term we prove that the existence of a bounded solution on r implies the existence of a weighted pseudo almost periodic solution our results extend the classical theorem due to massera on the existence of periodic solutions for linear periodic ordinary differential equations to illustrate the results we consider the lotka volterra model with diffusion

polar factorization and monotone rearrangement of vector valued functions given a probability space x p and a bounded domain r in rd equipped with the lebesgue measure 1 i normalized so that 10 i i it is shown under additional technical assumptions on x and q that for every vector valued function u e lp x p rd there is a unique polar factorization u v s where is a convex function defined on r and s is a measure preserving mapping from x p into q i i provided that u is nondegenerate in the sense that p u e 0 for each lebesgue negligible subset e of rd through this result the concepts of polar factorization of real matrices helmholtz decomposition of vector fields and nondecreasing rearrangements of real valued functions are unified the monge amgre equation is involved in the polar factorization and the proof relies on the study of an appropriate monge kantorovich problem

weighted pseudo almost periodic solutions to some differential equations abstract the paper considers some new classes of functions called weighted pseudo almost periodic functions which implement in a natural fashion the classical pseudo almost periodic functions due to zhang properties of these weighted pseudo almost periodic functions are discussed including a composition result for weighted pseudo almost periodic functions the results obtained are subsequently utilized to study the existence and uniqueness of a weighted pseudo almost periodic solution to the heat equation with dirichlet conditions

displacement convexity and minimal fronts at phase boundaries we show that certain free energy functionals that are not convex with respect to the usual convex structure on their domain of definition are strictly convex in the sense of displacement convexity under a natural change of variables we use this to show that in certain cases the only critical points of these functionals are minimizers this approach based on displacement convexity permits us to treat multicomponent systems as well as single component systems the developments produce new examples of displacement convex functionals and in the multi component setting jointly displacement convex functionals

weighted pseudo almost periodic solutions to a neutral delay integral equation of advanced type abstract this paper studies suitable sufficient conditions to ensure the existence and uniqueness of weighted pseudo almost periodic solutions to a neutral delay integral equation of advanced type introduced by t a burton in the literature the abstract results are then utilized to characterize weighted pseudo almost periodic solutions to the well known logistic equation

estimation of parameters in two dimensional transport equations a general approximation framework based on bicubic splines is developed for estimating temporally and spatially varying parameters in two dimensional transport equations the parameter estimation problem is first cast as an abstract infinite dimensional minimization problem then a sequence of approximate finite dimensional minimization problems is defined which yields a sequence of parameter estimates since convergence results relating the approximate problems to the full infinite dimensional problem are presented in 6 and 17 this paper will focus only on the computer implementation of our technique and the results of numerical tests using analytically generated data the technique is also applied to the analysis of actual biological data from an insect dispersal experiment in which the movement of cabbage root flies in the presence of a cabbage crop was studied

simultaneous identification of the spatio temporal dependent heat transfer coefficient and spatially dependent heat flux using an mcgm in a parabolic system abstract this paper aims to simultaneously identify the spatio temporal dependent heat transfer coefficient x t and the spatially dependent heat flux q x in a parabolic system the simultaneous identification problem is formulated as a constrained minimization problem using the output least squares method with tikhonov regularization the differentiability of the solution and adjoint equations are investigated to obtain the gradient formulae and determine the step lengths respectively to illustrate the efficiency accuracy and robustness of the proposed algorithm numerical results are investigated using the modified conjugate gradient method mcgm

surface tension in ising systems with kac potentials we consider an ising spin system with kac potentials in a torus of d d 2 and fix the temperature below its lebowitz penrose critical value we prove that when the kac scaling parameter vanishes the log of the probability of an interface becomes proportional to its area and the surface tension related to the proportionality constant converges to the van der waals surface tension the results are based on the analysis of the rate functionals for gibbsian large deviations and on the proof that they converge to the perimeter functional of geometric measure theory which extends the notion of area our considerations include nonsmooth interfaces proving that the gibbsian probability of an interface depends only on its area and not on its regularity

existence of weighted pseudo anti periodic solutions to some non autonomous differential equations abstract in this paper we first introduce two new concepts called respectively weighted pseudo periodicity and weighted pseudo anti periodicity which generalize respectively the well known notions of periodicity and that of anti periodicity basic properties of these new functions are discussed furthermore the existence of weighted pseudo anti periodic solutions to some damped non autonomous second order differential equations will be investigated to illustrate our abstract results the existence of weighted pseudo anti periodic solutions to a plate like equation is discussed

a nonlocal anisotropic model for phase transitions where u is a scalar density function on a domain of r and takes values in 1 1 w is a positive double well potential which vanishes at 1 and j is a positive possibly anisotropic interaction potential which vanishes at infinity see paragraph 1 2 for precise definitions the scalar function u represents the macroscopic density profile of a system which has two equilibrium pure phases described by the profiles u 1 and u 1 the integral w u at the right side of 1 1 forces a minimizer of f to take values close to 1 and 1 phase separation while the double integral represents an interaction energy which penalizes the spatial inhomogeneity of the system surface tension in equilibrium statistical mechanics functionals of the form 1 1 arise as free energies of continuum limits of ising spin systems on lattices in this setting u plays the role of a macroscopic magnetization density and j is a ferromagnetic kac potential see for instance 2 and references therein we underline the analogy with the more familiar gradient theory for phase transition proposed in 9 where the free energy of the system is of the form

existence of weighted pseudo almost periodic solutions to some classes of differential equations with sp weighted pseudo almost periodic coefficients abstract in this paper we introduce the concept of weighted pseudo almost periodicity in the sense of stepanov also called s p weighted pseudo almost periodicity and study its properties next we present a result on the existence of weighted pseudo almost periodic solutions to the n dimensional heat equation with s p weighted pseudo almost periodic coefficients

the estimation of l diffusion coefficients in the parabolic equations abstract the estimation of diffusion coefficients having only l bounds in parabolic equations is considered existence is obtained within a more general class of parabolic operators by means of g convergence the corresponding semi discrete problems are related to the original problem

almost automorphic solutions for some partial functional differential equations abstract in this work we study the existence of almost automorphic solutions for some partial functional differential equations we prove that the existence of a bounded solution on r implies the existence of an almost automorphic solution our results extend the classical known theorem by bohr and neugebauer on the existence of almost periodic solutions for inhomegeneous linear almost periodic differential equations we give some applications to hyperbolic equations and lotka volterra type equations used to describe the evolution of a single diffusive animal species

approximate periodic solutions of a nonlinear parabolic system and an identification problem this work continues our study in l lei identification of parameters through the approximate periodic solutions of a linear parabolic system preprint 2005 on the identification problem for the coefficients for the lower order terms in a parabolic system through its approximate periodic solutions different from the work in l lei identification of parameters through the approximate periodic solutions of a linear parabolic system preprint 2005 our system now is nonlinear and the coefficients to be detected are from the first order term from the application point of view we now try to determine the diffusion coefficients for the system by the observation over a subregion of the physical domain the existence and uniqueness problem of the approximate periodic solutions is studied in the first part of the paper

pseudo almost periodic solutions of some differential equations ii we first present some results about pseudo almost periodic functions then we use these results to show some theorems about existence and uniqueness of the pseudo almost periodic solutions of the linear and the quasi linear nonautonomous equations finally we set up some theorems of the existence of pseudo almost periodic solutions implying the existence of almost periodic solutions of general ordinary differential equation systems

displacement convexity for the generalized orthogonal ensemble the generalized orthogonal ensemble of n n real symmetric matrices x has probability measure nu n left dx right z n 1 exp left ntracev left x right right where dx is the product of lebesgue measure on the matrix entries and v left x right geqslant left 2 delta right log left x right with 0 the eigenvalue distribution is concentrated on left a mathord left vphantom a 2 right kern nulldelimiterspace 2 a mathord left vphantom a 2 right kern nulldelimiterspace 2 right for some a 0 or if the variance of the trace is o 1 n2 then the empirical distribution of eigenvalues converges weakly almost surely to some non random probability measure on a 2 a 2 as o left sqrt log n mathord left vphantom n n 2 right kern nulldelimiterspace n 2 right these conditions are satisfied for certain polynomial potentials the logarithmic energy is displacement convex as a functional on charge distributions with fixed mean along the real line when the trace distribution satisfies a logarithmic sobolev inequality or equivalently a quadratic transportation inequality the joint eigenvalue distributions and the limiting equilibrium measure likewise satisfy quadratic transportation inequalities in the sense of talagrand 24

a convexity principle for interacting gases a new set of inequalities is introduced based on a novel but natural interpolation between borel probability measures on r d using these estimates in lieu of convexity or rearrangement inequalities the existence and uniqueness problems are solved for a family of attracting gas models in these models the gas interacts with itself through a force which increases with distance and is governed by an equation of state p p relating pressure to density p d 1 d is assumed non decreasing for a d dimensional gas by showing that the internal and potential energies for the system are convex functions of the interpolation parameter an energy minimizing stateunique up to translationis proven to exist the concavity established for t pd q as a function of t 0 1 generalizes the brunnminkowski inequality from sets to measures 1997 academic press

almost automorphic and weighted pseudo almost automorphic solutions of semilinear evolution equations abstract in this paper applying the theory of semigroups of operators to evolution family and banach fixed point theorem we prove the existence and uniqueness of an a almost automorphic weighted pseudo almost automorphic mild solution of the semilinear evolution equation x t a t x t f t x t in banach space under conditions

parameter identification for a class of abstract nonlinear parabolic distributed parameter systems this paper studies the parameter identification problem of nonlinear abstract parabolic distributed parameter systems via variational method 1 based on the fundamental optimal control theory and the transposition method studied in 2 the existence of optimal parameter is proved and the necessary condition for the optimal parameter is established

an augmented lagrangian method for parameter identifications in parabolic systems the identification of parameters in parabolic systems is formulated as a constrained minimization problem combining the output least squares and the equation error method the minimization problem is then proved to be equivalent to the saddle point problem of an augmented lagrangian

the parameter estimation problem for parabolic equations and discontinuous observation operators parameter estimation problems are studied for a class of linear autonomous parabolic partial differential equations with various fit to data criteria which may be discontinuous with respect to the state variable we analyze the convergence of galerkin schemes approximating the optimization problems and generalize results to higher dimensional problems an example is then presented for the case of point observation fit to data criteria in higher dimensions finally discretization of coefficients is discussed for identification problems with variable coefficients