The Experts below are selected from a list of 8403 Experts worldwide ranked by ideXlab platform
T Yoshizawa - One of the best experts on this subject based on the ideXlab platform.
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almost periodic solutions in an Integrodifferential Equation
Proceedings of The Royal Society A: Mathematical Physical and Engineering Sciences, 1990Co-Authors: Y Hamaya, T YoshizawaAbstract:We consider a system of Integrodifferential Equations where f ( t , x ) and F ( t , s , x , y ) are almost periodic in t uniformly for parameters, and we assume that the system has a bounded solution u ( t ). To discuss the existence of an almost periodic solution, we consider the relationship between the total stability of u ( t ) with respect to a certain metric ρ and the separation condition with respect to ρ. Moreover, we discuss a sufficient condition for the existence of a positive almost periodic solution of a model of the dynamics of an n -species system.
Maurizio Grasselli - One of the best experts on this subject based on the ideXlab platform.
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existence uniqueness and longtime behavior for a nonlinear volterra Integrodifferential Equation
Differential and Integral Equations, 2000Co-Authors: Viorel Barbu, Pierluigi Colli, Gianni Gilardi, Maurizio GrasselliAbstract:We consider an initial and boundary value problem for a nonlinear Volterra Integrodifferential Equation. This Equation governs the evolution of a pair of state variables, u and θ, which are mutually related by a maximal monotone graph γ in R×R. The model can be viewed, for instance, as a generalized Stefan problem within the theory of heat conduction in materials with memory. Besides, it can be used for describing some diffusion processes in fractured media. The relation defined by γ is properly interpreted and generalized in terms of a subdifferential operator associated with γ and acting from H(Ω) to its dual space. Then, the generalized problem is formulated as an abstract Cauchy problem for a perturbation of a nonlinear semigroup, and existence and uniqueness of a solution (u, θ) can be proved via a fixed point argument whatever the maximal monotone graph γ is. Moreover, the meaning of γ as a pointwise relationship is recovered almost everywhere, in the case when γ is bounded on bounded subsets of R. Finally, under some other restrictions on γ, the longtime behavior of the solution is investigated, in a more specific context related to the generalized Stefan problem. AMS (MOS) Subject Classification. 45K05, 45D05, 45N05, 80A22, 76S05. 2 Barbu – Colli – Gilardi – Grasselli
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an identification problem for an abstract linear hyperbolic Integrodifferential Equation with applications
Journal of Mathematical Analysis and Applications, 1992Co-Authors: Maurizio GrasselliAbstract:Abstract We study the identification of a pair of time-dependent convolution kernels appearing in an abstract linear hyperbolic Integrodifferential Equation. We prove local (in time) existence, uniqueness, and continuous dependence on data results. We show the applications of such abstract results to viscoelasticity and electromagnetic wave propagation in rigid nonconducting dielectrics.
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an identification problem for a linear Integrodifferential Equation occurring in heat flow
Mathematical Methods in The Applied Sciences, 1992Co-Authors: Maurizio GrasselliAbstract:A linear Integrodifferential Equation describing the heat flow in a material with memory is considered. This Equation contains a pair of time-dependent convolution kernels that are unknown. Such kernels are recovered by using an overdetermined set of data. A local existence theorem for small times and the continuous dependence of the solutions on the data are shown.
Jaan Janno - One of the best experts on this subject based on the ideXlab platform.
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inverse problems for a parabolic Integrodifferential Equation in a convolutional weak form
Abstract and Applied Analysis, 2013Co-Authors: Kairi Kasemets, Jaan JannoAbstract:We deduce formulas for the Frechet derivatives of cost functionals of several inverse problems for a parabolic Integrodifferential Equation in a weak formulation. The method consists in the application of an integrated convolutional form of the weak problem and all computations are implemented in regular Sobolev spaces.
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discretization and regularization of an inverse problem related to a quasilinear hyperbolic Integrodifferential Equation
Inverse Problems, 1997Co-Authors: Jaan JannoAbstract:An inverse problem for a one-dimensional quasilinear hyperbolic Integrodifferential Equation is reduced to a system of hyperbolic and second-kind integral Equations. The obtained system is discretized by means of the method of finite differences. The convergence of the difference scheme in the case of small data is proved and the regularization of the inverse problem is discussed.
Y Hamaya - One of the best experts on this subject based on the ideXlab platform.
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almost periodic solutions in an Integrodifferential Equation
Proceedings of The Royal Society A: Mathematical Physical and Engineering Sciences, 1990Co-Authors: Y Hamaya, T YoshizawaAbstract:We consider a system of Integrodifferential Equations where f ( t , x ) and F ( t , s , x , y ) are almost periodic in t uniformly for parameters, and we assume that the system has a bounded solution u ( t ). To discuss the existence of an almost periodic solution, we consider the relationship between the total stability of u ( t ) with respect to a certain metric ρ and the separation condition with respect to ρ. Moreover, we discuss a sufficient condition for the existence of a positive almost periodic solution of a model of the dynamics of an n -species system.
A Lemarchand - One of the best experts on this subject based on the ideXlab platform.
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existence of solutions of a partial Integrodifferential Equation with thermostat and time delay
Abstract and Applied Analysis, 2014Co-Authors: Carlo Bianca, Luca Guerrini, A LemarchandAbstract:This paper deals with the mathematical analysis of a retarded partial Integrodifferential Equation that belongs to the class of thermostatted kinetic Equations with time delay. Specifically, the paper is devoted to the proof of the existence and uniqueness of mild solutions of the related Cauchy problem. The main result is obtained by employing integration along the characteristic curves and successive approximations sequence arguments. Applications and perspective are also discussed within the paper.