Title of article
On a class of nonlinear parabolic equations with natural growth in non-reflexive Musielak spaces
Author/Authors
Bourahma, Mohamed Laboratory of mathematical analysis and applications (LAMA) - Department of mathematics - Faculty of Sciences Dhar el Mahraz - Sidi Mohamed Ben Abdellah University, Morocco , Deval, Sidi Mohamed Laboratory of mathematical analysis and applications (LAMA) - Department of mathematics - Faculty of Sciences Dhar el Mahraz - Sidi Mohamed Ben Abdellah University, Morocco , Bennouna, Jaouad Laboratory of mathematical analysis and applications (LAMA) - Department of mathematics - Faculty of Sciences Dhar el Mahraz - Sidi Mohamed Ben Abdellah University, Morocco , Benkirane, Abdelmoujib Laboratory of mathematical analysis and applications (LAMA) - Department of mathematics - Faculty of Sciences Dhar el Mahraz - Sidi Mohamed Ben Abdellah University, Morocco
Pages
27
From page
1207
To page
1233
Abstract
An existence result of renormalized solutions for nonlinear parabolic Cauchy-Dirichlet problems whose model
⎧⎩⎨⎪⎪⎪⎪⎪⎪∂b(x,u)∂t−divA(x,t,u,∇u)−divΦ(x,t,u)=fb(x,u)(t=0)=b(x,u0)u=0 in Ω×(0,T) in Ω on ∂Ω×(0,T).
is given in the non reflexive Musielak spaces, where b(x,⋅) is a strictly increasing C1-function for every x∈Ω with b(x,0)=0, the lower order term Φ is a non coercive Carath'{e}odory function satisfying only a natural growth condition described by the appropriate Musielak function φ and f is an integrable data.
Keywords
Parabolic problems , Musielak spaces , Renormalized solutions , natural growth
Journal title
International Journal of Nonlinear Analysis and Applications
Serial Year
2021
Record number
2607843
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