ASYMPTOTIC HOMOGENIZATION IN A PARABOLIC SEMILINEAR PROBLEM WITH PERIODIC COEFFICIENTS AND INTEGRABLE INITIAL DATA

作     者：Rogerio Luiz Quintino de OLIVEIRA JUNIOR 

作者机构：Instituto de Matema'tica e Estat' stica Universidade do Estado do R.de Janeiro Rua S ao Francisco Xavier524 - Pavilha o Reitor Joa o Lyra Filho 6oandar bl.B 20559-900 Rio de Janeiro R.J. Brazil 

出 版 物：《Acta Mathematica Scientia》 (数学物理学报（B辑英文版）)

年 卷 期：2013年第33卷第5期

页      面：1275-1292页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Supported by CNPq-Conselho Nacional de Desenvolvimento Cient'fico e Tecnológico 

主　　题：homogenization similinear parabolic equation integrable initial data matrix with periodic coefficient large time behavior 

摘      要：In this paper, we study the large time behavior of solutions of the parabolic semilinear equation δtu-div（a（x）△↓u） = -｜u｜^αu in （0,∞） × R^N, where α 〉 0 is constant and a∈ Cb^1（R^N） is a symmetric periodic matrix satisfying some ellipticity *** an integrable initial data u0 and α ∈ （2/N, 3/N）, we prove that the large time behavior of solutions is given by the solution U（t, x） of the homogenized linear problem δtU-div（a^h△↓U）=0,U（0） = C, where a^h is the homogenized matrix of a（x）, C is a positive constant and δ is the Dirac measure at 0.