# On some Improperly Posed Problem for a Degenerate Nonlinear Parabolic Equation

### Kazuya Hayasida

Kanazawa University, Japan

## 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.

## Cite this article

Kazuya Hayasida, On some Improperly Posed Problem for a Degenerate Nonlinear Parabolic Equation. Z. Anal. Anwend. 19 (2000), no. 2, pp. 395–413

DOI 10.4171/ZAA/958