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.