ON THE CONTINUATION OF SOLUTIONS OF NON-AUTONOMOUS SEMILINEAR PARABOLIC PROBLEMS

被引：1

作者：

Carvalho, Alexandre N. ^{[1
]}

Cholewa, Jan W. ^{[2
]}

Nascimento, Marcelo J. D. ^{[3
]}

机构：

[1] Univ Sao Paulo, Inst Ciencias Matemat & Comp, Dept Matemat, BR-13560970 Sao Paulo, Brazil

[2] Silesian Univ, Inst Math, PL-40007 Katowice, Poland

[3] Univ Fed Sao Carlos, Dept Matemat, BR-13565905 Sao Paulo, Brazil

来源：

PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY | 2016年 / 59卷 / 01期

基金：

巴西圣保罗研究基金会;

关键词：

abstract parabolic equations; continuation of solutions; critical exponents; DAMPED WAVE-EQUATIONS; INTERPOLATION; BOUNDARY;

D O I：

10.1017/S001309151400039X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study non-autonomous parabolic equations with critical exponents in a scale of Banach spaces E-sigma, sigma is an element of [0,1 + mu). We consider a suitable E1+epsilon-solution and describe continuation properties of the solution. This concerns both a situation when the solution can be continued as an E1+epsilon-solution and a situation when the E1+epsilon-norm of the solution blows up, in which case a piecewise E1+epsilon-solution is constructed.

引用

页码：17 / 55

页数：39

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