Acta mathematica scientia, Series B >
EXISTENCE OF POSITIVE SOLUTIONS FOR A CLASS OF PARABOLIC EQUATIONS WITH NATURAL GROWTH TERMS AND L1 DATA
Received date: 2013-04-02
Revised date: 2013-12-10
Online published: 2014-07-20
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.
Key words： renormalized solutions; natural growth terms; L1 data
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 . DOI: 10.1016/S0252-9602(14)60074-6
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