Publication Cover
Applicable Analysis
An International Journal
Volume 81, 2002 - Issue 3
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Original Articles

An Inverse Coefficient Problem for an Integro-differential Equation

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Pages 725-752 | Published online: 09 Sep 2010
 

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.

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