Non-stability result of entropy solutions for nonlinear parabolic problems with singular measures

2019 ◽  
Vol 5 (1) ◽  
pp. 149-174 ◽  
Author(s):  
Mohammed Abdellaoui ◽  
Elhoussine Azroul
Keyword(s):  
Stability Result ◽  
Entropy Solutions ◽  
Parabolic Problems ◽  
Nonlinear Parabolic Problems ◽  
Singular Measures ◽  
Nonlinear Parabolic

scholarly journals Entropy solutions for nonlinear parabolic inequalities involving measure data in Musielak-Orlicz-Sobolev spaces

2018 ◽  
Vol 36 (2) ◽  
pp. 199 ◽  
Author(s):  
Talha Abdeslam ◽  
Abdelmoujib Benkirane ◽  
Mohamed Saad Bouh Elemine Vall
Keyword(s):  
Sobolev Spaces ◽  
Existence Result ◽  
Entropy Solutions ◽  
Parabolic Problems ◽  
Measure Data ◽  
Nonlinear Parabolic Problems ◽  
Nonlinear Parabolic ◽  
Parabolic Inequalities

In this paper, we study an existence result of entropy solutions for some nonlinear parabolic problems in the Musielak-Orlicz-Sobolev spaces.

scholarly journals Existence of entropy solutions in Musielak Orlicz spaces via a sequence of penalized equations

2019 ◽  
Vol 38 (6) ◽  
pp. 203-238
Author(s):  
Mhamed Elmassoudi ◽  
Ahmed Aberqi ◽  
Jaouad Bennouna
Keyword(s):  
Orlicz Space ◽  
Existence Result ◽  
Orlicz Spaces ◽  
Growth Conditions ◽  
Entropy Solutions ◽  
Parabolic Problems ◽  
Pseudomonotone Operator ◽  
Nonlinear Parabolic Problems ◽  
Orlicz Functions ◽  
Nonlinear Parabolic

This paper, is devoted to an existence result of entropy unilateral solutions for the nonlinear parabolic problems with obstacle in Musielak- Orlicz--spaces:$$ \partial_{t}u + A(u) + H(x,t,u,\nabla u) =f + div(\Phi(x,t,u))$$and $$ u\geq \zeta \,\,\mbox{a.e. in }\,\,Q_T.$$Where $A$ is a pseudomonotone operator of Leray-Lions type defined in the inhomogeneous Musielak-Orlicz space $W_{0}^{1,x}L_{\varphi}(Q_{T})$,$H(x,t,s,\xi)$ and $\phi(x,t,s)$ are only assumed to be Crath\'eodory's functions satisfying only the growth conditions prescribed by Musielak-Orlicz functions $\varphi$ and $\psi$ which inhomogeneous and does not satisfies $\Delta_2$-condition. The data $f$ and $u_{0}$ are still taken in $L^{1}(Q_T)$ and $L^{1}(\Omega)$.

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