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

doi:10.1016/S0252-9602(13)60080-6

数学物理学报(英文版) ›› 2013, Vol. 33 ›› Issue (5): 1275-1292.doi: 10.1016/S0252-9602(13)60080-6

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

Rogerio Luiz Quintino de OLIVEIRA JUNIOR

Instituto de Matem´atica e Estatistica, Universidade do Estado do R. de Janeiro, Rua Sao Francisco Xavier, 524 - Pavilhao Reitor Jo˜ao Lyra Filho, 6o andar, bl. B 20559-900, Rio de Janeiro, R.J., Brazil

收稿日期:2012-02-03 修回日期:2012-10-15 出版日期:2013-09-20 发布日期:2013-09-20
基金资助:
Supported by CNPq-Conselho Nacional de Desen-volvimento Cient´?fico e Tecnol´ogico.

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

Rogerio Luiz Quintino de OLIVEIRA JUNIOR

Instituto de Matem´atica e Estatistica, Universidade do Estado do R. de Janeiro, Rua S˜ao Francisco Xavier, 524 - Pavilh˜ao Reitor Jo˜ao Lyra Filho, 6o andar, bl. B 20559-900, Rio de Janeiro, R.J., Brazil

Received:2012-02-03 Revised:2012-10-15 Online:2013-09-20 Published:2013-09-20
Supported by:
Supported by CNPq-Conselho Nacional de Desen-volvimento Cient´?fico e Tecnol´ogico.

摘要/Abstract

摘要：

In this paper, we study the large time behavior of solutions of the parabolic semilinear equation @tu − div(a(x)∇u) = −|u| u in (0,∞) × RN, where > 0 is constant and a ∈ C1 b (RN) is a symmetric periodic matrix satisfying some ellipticity assumptions. Considering an integrable initial data u0 and ∈ (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 @tU − div(ah∇U) = 0, U(0) = C, where ah is the homogenized matrix of a(x), C is a positive constant and is the Dirac measure at 0.

关键词: homogenization, similinear parabolic equation, integrable initial data, ma-trix with periodic coefficient, large time behavior

Key words: homogenization, similinear parabolic equation, integrable initial data, ma-trix with periodic coefficient, large time behavior

中图分类号:

35K61

Rogerio Luiz Quintino de OLIVEIRA JUNIOR. ASYMPTOTIC HOMOGENIZATION IN A PARABOLIC SEMILINEAR PROBLEM WITH PERIODIC COEFFICIENTS AND#br# INTEGRABLE INITIAL DATA[J]. 数学物理学报(英文版), 2013, 33(5): 1275-1292.

Rogerio Luiz Quintino de OLIVEIRA JUNIOR. ASYMPTOTIC HOMOGENIZATION IN A PARABOLIC SEMILINEAR PROBLEM WITH PERIODIC COEFFICIENTS AND#br# INTEGRABLE INITIAL DATA[J]. Acta mathematica scientia,Series B, 2013, 33(5): 1275-1292.

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

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

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