A GLOBAL IN TIME EXISTENCE AND UNIQUENESS RESULT FOR A SEMILINEAR INTEGRODIFFERENTIAL PARABOLIC INVERSE PROBLEM IN SOBOLEV SPACES

2007 ◽  
Vol 17 (04) ◽  
pp. 537-565 ◽  
Author(s):  
FABRIZIO COLOMBO ◽  
DAVIDE GUIDETTI
Keyword(s):  
Inverse Problem ◽  
Heat Conduction ◽  
Existence And Uniqueness ◽  
Parabolic Problem ◽  
Uniqueness Result ◽  
Convolution Kernel ◽  
Materials With Memory ◽  
Time Existence ◽  
With Memory ◽  
Abstract Existence

We prove a global in time abstract existence and uniqueness result for a general parabolic problem of reconstruction of a convolution kernel. The result is, in particular, applicable to the theory of heat conduction for materials with memory.

On linear theory of heat conduction in materials with memory. Existence and uniqueness theorems for the final value problem

1977 ◽  
Vol 76 (2) ◽  
pp. 119-137 ◽  
Author(s):  
H. Grabmüller
Keyword(s):  
Heat Conduction ◽  
Existence And Uniqueness ◽  
Sufficient Conditions ◽  
Function Algebra ◽  
Fading Memory ◽  
Uniqueness Of Solutions ◽  
Materials With Memory ◽  
Solvability Conditions ◽  
Broad Variety ◽  
With Memory

SynopsisAn improperly posed problem is studied for a linear partial integro-differential equation of convolution type on the semi-axis. The problem originates from a generalised process of heat conduction in materials with fading memory, where the temperature of the material has to be determined for prescribed homogeneous boundary conditions and for a given final temperature distribution. By using eigenfunctions of the n-dimensional Laplacian, the problem is reduced to a family of equivalent initial-value problems for ordinary integro-differential equations; the latter are treated by the method of factorisation in a suitable function algebra. Sufficient conditions for the existence and uniqueness of solutions to the original problem are obtained in terms of the solvability conditions of the reduced problems. The whole analysis is performed simultaneously in a broad variety of spaces consisting of functions with an exponential growth rate (in the time variable) at infinity. One of the main advantages in the present approach is that solutions, if they exist, can always be computed explicitly.

scholarly journals Asymptotic Periodicity for a Class of Partial Integrodifferential Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-18 ◽  
Author(s):  
Alejandro Caicedo ◽  
Claudio Cuevas ◽  
Hernán R. Henríquez
Keyword(s):  
Heat Conduction ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Integral Equations ◽  
Integrodifferential Equations ◽  
Materials With Memory ◽  
Asymptotic Periodicity ◽  
With Memory ◽  
Equations With Delay

We study the existence of S-asymptotically ω-periodic solutions for a class of abstract partial integro-differential equations and for a class of abstract partial integrodifferential equations with delay. Applications to integral equations arising in the study of heat conduction in materials with memory are shown.

Stochastic non-resistive magnetohydrodynamic system with L\'{e}vy noise

2017 ◽  
Vol 25 (3) ◽  
Author(s):  
Utpal Manna ◽  
Manil T. Mohan ◽  
Sivaguru S. Sritharan
Keyword(s):  
Existence And Uniqueness ◽  
Uniqueness Result ◽  
Three Dimensions ◽  
Mhd Equations ◽  
Lévy Noise ◽  
Magnetohydrodynamic System ◽  
Levy Noise ◽  
Time Existence ◽  
Maximal Time ◽  
The Ideal

AbstractIn this work we prove the existence and uniqueness of path-wise solutions up to a maximal time for the viscous, non-resistive stochastic magnetohydrodynamic system perturbed by Lévy noise in two and three dimensions. The local-in-time existence and uniqueness result for the ideal and non-viscous MHD equations with Lévy noise is also addressed.

scholarly journals A degenerate pseudo-parabolic equation with memory

2019 ◽  
Vol 10 (1) ◽  
pp. 71-77
Author(s):  
Micol Amar ◽  
Daniele Andreucci ◽  
Roberto Gianni ◽  
Claudia Timofte
Keyword(s):  
Parabolic Equation ◽  
Composite Materials ◽  
Electrical Conduction ◽  
Existence And Uniqueness ◽  
Parabolic Problem ◽  
Beltrami Operator ◽  
Differential Systems ◽  
With Memory

Abstract We prove the existence and uniqueness for a degenerate pseudo-parabolic problem with memory. This kind of problem arises in the study of the homogenization of some differential systems involving the Laplace-Beltrami operator and describes the effective behaviour of the electrical conduction in some composite materials.

An inverse problem in the theory of materials with memory

1988 ◽  
Vol 12 (12) ◽  
pp. 1317-1335 ◽  
Author(s):  
A. Lorenzi ◽  
E. Sinestrari
Keyword(s):  
Inverse Problem ◽  
Materials With Memory ◽  
With Memory
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