具有低阶项和可积数据的抛物各向异性问题

IF 0.7 Q3 MATHEMATICS, APPLIED

Differential Equations & Applications Pub Date : 2020-01-01 DOI:10.7153/dea-2020-12-26

M. Chrif, S. E. Manouni, H. Hjiaj

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引用次数: 1

摘要

本文研究了一类具有各向异性生长条件的含Leray-Lions型算子的二阶拟线性抛物型方程。通过一个近似论证，我们建立了各向异性抛物Sobolev空间框架中，当初始条件和数据仅可积时，熵解的存在性。此外，我们还证明了熵解与重整化解重合。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Parabolic anisotropic problems with lower order terms and integrable data

In this paper we are concerned with the study of a class of second-order quasilinear parabolic equations involving Leray-Lions type operators with anisotropic growth conditions. By an approximation argument, we estabilsh the existence of entropy solutions in the framework of anisotropic parabolic Sobolev spaces when the initial condition and the data are assumed to be merely integrable. In addition, we prove that entropy solutions coincide with the renormalized solutions.

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Differential Equations & Applications MATHEMATICS, APPLIED-

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