ON EXISTENCE AND UNIQUENESS CLASSES FOR THE CAUCHY PROBLEM FOR PARABOLIC EQUATIONS OF THE P-LAPLACE TYPE

被引：6

作者：

Surnachev, Mikhail D. ^{[1
]}

Zhikov, Vasily V. ^{[2
]}

机构：

[1] MV Keldysh Appl Math Inst, Computat Aeroacoust Lab, Moscow 125047, Russia

[2] Vladimir State Univ, Dept Math, Vladimir 600000, Russia

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2013年 / 12卷 / 04期

关键词：

Cauchy problem; p-Laplacian; existence; uniqueness; energy classes; POROUS-MEDIUM EQUATION; COMPENSATED COMPACTNESS; INITIAL TRACES; LEMMAS;

D O I：

10.3934/cpaa.2013.12.1783

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove the existence and uniqueness of global solutions to the Cauchy problem for a class of parabolic equations of the p-Laplace type. In the singular case p < 2 there are no restrictions on the behaviour of solutions and initial data at infinity. In the degenerate case p > 2 we impose a restriction on growth of solutions at infinity to obtain global existence and uniqueness. This restriction is given in terms of weighted energy classes with power-like weights.

引用

页码：1783 / 1812

页数：30

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