J. Nonl. Evol. Equ. Appl. 2017 (3), pp. 27-48, published on July 31, 2017:

Nonlinear parabolic equations with diffuse measure data

A. Marah, H. Redwane

Faculté des Sciences Juridiques, Economiques et Sociales. Université Hassan 1, B.P. 764. Settat. Morocco

Received on August 29, 2016
Accepted on September 1, 2016 (with modifications)

Communicated by Alexander Pankov

Abstract.  We give an existence result of a renormalized solution for a class of nonlinear parabolic equations
∂b(x, u)/∂t − div( a(x, t, ∇u) ) = μ,
where the right side is a diffuse measure and where b(x, u) is an unbounded function of u and where −div(a(x, t, ∇u)) is a Leray–Lions type operator with growth of |∇u|p−1 in ∇u.
Keywords:Nonlinear parabolic equations. Existence. Measure. Renormalized solutions.
2010 Mathematics Subject Classification:   47A15, 46A32, 47D20.

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