On some Improperly Posed Problem for a Degenerate Nonlinear Parabolic Equation

Abstract

We consider the non-characteristic Cauchy problem for the degenerate nonlinear parabolic equation$|u|^{\\alpha}u_t – \\Delta u – \\gamma |u|^{–\\beta} u = 0$ under some assumptions on$\\alpha, \\beta$ and $\\gamma$. The problem is improperly posed in the sense of Hadamard. We derive for such solutions an estimate in terms of the Cauchy data and a prescribed bound of the solution.