The Cauchy problem for a class of quasilinear parabolic equations

被引：1

作者：

Alkis S. Tersenov

Aris S. Tersenov

机构：

[1] University of Crete,Department of Mathematics

[2] FO.R.T.H.,Institute of Appl. and Comp. Mathematics

来源：

Annali di Matematica Pura ed Applicata | 2003年 / 182卷 / 3期

关键词：

quasilinear parabolic equations; Hamilton–Jacobi equation;

D O I：

10.1007/s10231-002-0070-0

中图分类号：

学科分类号：

摘要：

The present paper is concerned with the Cauchy problem for the parabolic equation ut+H(t,x,u,∇u)=εΔu. New conditions guaranteeing the global classical solvability are formulated. Moreover, it is shown that the same conditions guarantee the global existence of the Lipschitz continuous viscosity solution for the related Hamilton–Jacobi equation.

引用

页码：325 / 336

页数：11

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