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

Abstract

Abstract:

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

CLC Number:

35K55

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

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