JournalszaaVol. 19, No. 2pp. 395–413

On some Improperly Posed Problem for a Degenerate Nonlinear Parabolic Equation

  • Kazuya Hayasida

    Kanazawa University, Japan
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Abstract

We consider the non-characteristic Cauchy problem for the degenerate nonlinear parabolic equationuαutΔuγuβu=0|u|^{\alpha}u_t – \Delta u – \gamma |u|^{–\beta} u = 0 under some assumptions onα,β\alpha, \beta and γ\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