An inverse coefficient problem for a quasilinear parabolic equation with nonlocal boundary conditions

Fatma Kanca,Irem Baglan

doi:10.1186/1687-2770-2013-213

Abstract

In this paper the inverse problem of finding the time-dependent coefficient of heat capacity together with the 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 identification of 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

Denote the domain D by

Definition The pair {p(t), u(x, t)} from the class C[ , T] × (C , (D) ∩ C , (D)), for which conditions ( )-( ) are satisfied and p(t) ≥ on the interval [ , T], is called the classical solution of inverse problem ( )-( ). Inverse problems for parabolic equations with nonlocal boundary conditions are investigated in [ – ]. In [ ] the boundary condition is nonlocal but the problem is linear and the existence and the uniqueness of the classical solution is obtained locally using a fixed point theorem. In Section , the existence and uniqueness of the solution of inverse problem ( )-( ) is proved by using the Fourier method and the iteration method. The systems of these functions arise in [ ] for the solution of a nonlocal boundary value problem in heat conduction.

MA T

Nx and τ