EXISTENCE OF POSITIVE SOLUTIONS FOR A CLASS OF PARABOLIC EQUATIONS WITH NATURAL GROWTH TERMS AND L1 DATA

doi:10.1016/S0252-9602(14)60074-6

数学物理学报(英文版) ›› 2014, Vol. 34 ›› Issue (4): 1127-1144.doi: 10.1016/S0252-9602(14)60074-6

EXISTENCE OF POSITIVE SOLUTIONS FOR A CLASS OF PARABOLIC EQUATIONS WITH NATURAL GROWTH TERMS AND L¹ DATA

Kaouther AMMAR, Hicham REDWANE

Department of Mathematics, Faculty of sciences, Taibah University, P.O. Box 344 Al Madinah, Saudi Arabia|Facult´e des Sciences Juridiques, Economiques et Sociales, Universit´e Hassan 1, B.P. 784, Settat, Morocco

收稿日期:2013-04-02 修回日期:2013-12-10 出版日期:2014-07-20 发布日期:2014-07-20
基金资助:
EXISTENCE OF POSITIVE SOLUTIONS FOR A CLASS OF PARABOLIC EQUATIONS WITH NATURAL GROWTH TERMS AND L¹ DATA

EXISTENCE OF POSITIVE SOLUTIONS FOR A CLASS OF PARABOLIC EQUATIONS WITH NATURAL GROWTH TERMS AND L¹ DATA

Kaouther AMMAR, Hicham REDWANE

Department of Mathematics, Faculty of sciences, Taibah University, P.O. Box 344 Al Madinah, Saudi Arabia|Facult´e des Sciences Juridiques, Economiques et Sociales, Universit´e Hassan 1, B.P. 784, Settat, Morocco

Received:2013-04-02 Revised:2013-12-10 Online:2014-07-20 Published:2014-07-20

摘要/Abstract

摘要：

We study a class of nonlinear parabolic equations of the type:
∂b(u)/∂t− div(a(x, t, u)∇u)+ g(u)|∇u|² = f,
where the right hand side belongs to L¹(Q), b is a strictly increasing C¹-function and −div(a(x, t, u)∇u) is a Leray-Lions operator. The function g is just assumed to be con-tinuous on R and to satisfy a sign condition. Without any additional growth assumption on u, we prove the existence of a renormalized solution.

关键词: renormalized solutions, natural growth terms, L¹ data

Abstract:

Key words: renormalized solutions, natural growth terms, L¹ data

中图分类号:

35K55

Kaouther AMMAR, Hicham REDWANE. EXISTENCE OF POSITIVE SOLUTIONS FOR A CLASS OF PARABOLIC EQUATIONS WITH NATURAL GROWTH TERMS AND L¹ DATA[J]. 数学物理学报(英文版), 2014, 34(4): 1127-1144.

Kaouther AMMAR, Hicham REDWANE. EXISTENCE OF POSITIVE SOLUTIONS FOR A CLASS OF PARABOLIC EQUATIONS WITH NATURAL GROWTH TERMS AND L¹ DATA[J]. Acta mathematica scientia,Series B, 2014, 34(4): 1127-1144.

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EXISTENCE OF POSITIVE SOLUTIONS FOR A CLASS OF PARABOLIC EQUATIONS WITH NATURAL GROWTH TERMS AND L¹ DATA

EXISTENCE OF POSITIVE SOLUTIONS FOR A CLASS OF PARABOLIC EQUATIONS WITH NATURAL GROWTH TERMS AND L¹ DATA

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