J. Nonl. Evol. Equ. Appl. 2019 (6), pp. 95-114, published on May 31, 2020:

Nonlinear parabolic equation with variable exponents and diffuse measure data

H. Redwane

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

Received on July 17, 2018, revised version on November 27, 2019
Accepted on November 29, 2019

Communicated by Ti-Jun Xiao

Abstract.  We study the existence of solutions of the nonlinear parabolic equation with variable exponents of the type:
∂b(x, u)/∂t − div(a(x, t, ∇u)) = μ   in   Ω × (0, T),
where the right side is a diffuse measure and where b(x, u) is unbounded function of u and where −div(a(x, t, ∇u)) is a Leray–Lions type operator with growth |∇u|p(.)−1 in ∇u.
Keywords:Nonlinear parabolic equations. Existence. Measure. Renormalized solutions.
2010 Mathematics Subject Classification:   Primary 47A15; Secondary 46A32, 47D20.

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