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
收藏
页码：17 / 55
页数：39
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