Abstract
In this paper the inverse problem of finding the time-dependent coefficient of heat capacity together with the solution of heat equation with nonlocal boundary conditions is considered. Under some natural regularity and consistency conditions on the input data, the existence, uniqueness and continuous dependence upon the data of the solution are shown. Some considerations on the numerical solution for this inverse problem are presented with an example.
Highlights
Denote the domain D byD := { < x
The problem of identifying a coefficient in a nonlinear parabolic equation is an interesting problem for many scientists [ – ]
Inverse problems for parabolic equations with nonlocal boundary conditions are investigated in [, ]. This kind of conditions arise from many important applications in heat transfer, life sciences, etc
Summary
Inverse problems for parabolic equations with nonlocal boundary conditions are investigated in [ , ]. This kind of conditions arise from many important applications in heat transfer, life sciences, etc. Y k(x) = ( – x) sin( π kx), k = , , The systems of these functions arise in [ ] for the solution of a nonlocal boundary value problem in heat conduction. Applying the Cauchy inequality and the Lipschitz condition to the last equation and taking the maximum of both sides of the last inequality yields the following: u( )(t). Applying the Cauchy inequality, the Hölder inequality, the Lipschitz condition and the Bessel inequality to the last equation, we obtain u( )(t) – u( )(t) B ≤.
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