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Zeitschrift für Analysis und ihre Anwendungen


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Volume 19, Issue 2, 2000, pp. 395–413
DOI: 10.4171/ZAA/958

Published online: 2000-06-30

On some Improperly Posed Problem for a Degenerate Nonlinear Parabolic Equation

Kazuya Hayasida[1]

(1) Kanazawa University, Japan

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.

Keywords: Degenerate parabolic equations, non-characteristic Cauchy problem, fast diffusion

Hayasida Kazuya: On some Improperly Posed Problem for a Degenerate Nonlinear Parabolic Equation. Z. Anal. Anwend. 19 (2000), 395-413. doi: 10.4171/ZAA/958