An Inverse Coefficient Problem for an Integro-differential Equation

Autor:	Thomas S. Shores, A. M. Denisov
Rok vydání:	2002
Předmět:	Partial differential equation Integro-differential equation Applied Mathematics Mathematical analysis Inverse Order (ring theory) Boundary value problem Function (mathematics) Uniqueness Inverse problem Analysis Mathematical physics Mathematics
Zdroj:	Applicable Analysis. 81:725-752
ISSN:	1563-504X 0003-6811
DOI:	10.1080/0003681021000004393
Popis:	In this article we consider the inverse coefficient problem of recovering the function { ( x ) system of partial differential equations that can be reduced to a second order integro-differential equation $ -u_{xx} + c(x)u_{x} + d\phi (x)u-\gamma d\phi (x)\int _{0}^{t}e^{-\gamma (t-\tau )}u(x,\tau )\, d\tau = 0 $ with boundary conditions. We prove the existence and uniqueness of solutions to the inverse problem and develop a numerical algorithm for solving this problem. Computational results for some examples are presented.
Databáze:	OpenAIRE
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