Determination of a diffusion coefficient in a quasilinear parabolic equation

Abstract

This paper investigates the inverse problem of finding the time-dependent diffusion coefficient in a quasilinear parabolic equation with the nonlocal boundary and integral overdetermination conditions. Under some natural regularity and consistency conditions on the input data the existence, uniqueness and continuously dependence upon the data of the solution are shown. Finally, some numerical experiments are presented.

Keywords

• heat equation
• inverse problem
• nonlocal boundary condition
• integral overdetermination condition
• time-dependent diffusion coefficient
• 35k59
• 35r30