Uniqueness of the Solution of an lnverse Problem for a Quasilinear Parabolic Equation in Divergence Form

Abstract

The quasilinear parabolic differential equation $u_t=\mathrm{div}(a(u)\mathrm{grad}u)$ with a constant initial condition and a boundary condition of the first kind is considered where $a$ is a positive analytic function of $u$. Under some additional assumptions on u a uniqueness theorem for the determination of the coefficient a is proved.