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 $L^{1}(\Omega)$.

scholarly journals A few results on some nonlinear parabolic problems in Orlicz-Sobolev spaces

2018 ◽  
Vol 4 (2) ◽  
pp. 158-170
Author(s):  
Hicham Redwane
Keyword(s):  
Sobolev Spaces ◽  
Parabolic Problems ◽  
Renormalized Solutions ◽  
Nonlinear Parabolic Problems ◽  
Nonlinear Parabolic ◽  
Carathéodory Functions

AbstractIn this paper, we present our results (see our papers), which concern the existence of the renormalized solutions for equations of the type:$${{\partial b(x,u)} \over {\partial t}} - {\rm{div}}\left( {a(x,t,u,\nabla u)} \right) - {\rm{div}}\left( {\Phi \left( {x,t,u} \right)} \right) = f\,\,\,{\rm{in}}\,Q = \Omega \times (0,T),$$where b(x, ·) is a strictly increasing C1-function for any x ∈ Δ, a(x, t, s, ξ) and Φ(x, t, s) are a Carathéodory functions. The function f is in L1(Q).

Blow-up Results for Parabolic Inequalities with Chipot–Weissler Nonlinearity in the Gradient Term

2004 ◽  
Vol 4 (2) ◽  
Author(s):  
Anna Maria Piccirillo ◽  
Luisa Toscano ◽  
Speranza Toscano
Keyword(s):  
Positive Solutions ◽  
Wide Class ◽  
Blow Up ◽  
Parabolic Problems ◽  
Gradient Term ◽  
Nonlinear Parabolic Problems ◽  
Nonlinear Parabolic ◽  
Open Question ◽  
Parabolic Inequalities

AbstractWe obtain blow-up results for a wide class of nonlinear parabolic problems with nonlinearity of the Chipot-Weissler type in the gradient term. Some of these answer an open question concerning the nonexistence of positive solutions to the problemwhere λ > 0 is small, u

scholarly journals Strongly nonlinear parabolic problems in Musielak-Orlicz-Sobolev spaces

2014 ◽  
Vol 33 (1) ◽  
pp. 191 ◽  
Author(s):  
Mohamed Leimne Ahmed Oubeid ◽  
A. Benkirane ◽  
M. Sidi El Vally
Keyword(s):  
Sobolev Spaces ◽  
Existence Of Solutions ◽  
Parabolic Problems ◽  
Nonlinear Parabolic Problems ◽  
Strongly Nonlinear ◽  
Nonlinear Parabolic

We prove in this paper the existence of solutions of strongly nonlinear parabolic problems in Musielak-Orlicz-Sobolev spaces. An approximation and a compactness results in inhomogeneous Musielak-Orlicz-Sobolev spaces have also been provided.

scholarly journals Renormalized solutions for nonlinear parabolic problems with L1−data in orlicz-sobolev spaces

2017 ◽  
Vol 35 (1) ◽  
pp. 57 ◽  
Author(s):  
Youssef El hadfi ◽  
Abdelmoujib Benkirane ◽  
Mostafa El moumni
Keyword(s):  
Sobolev Spaces ◽  
Lower Order ◽  
Parabolic Equations ◽  
Existence Result ◽  
Nonlinear Parabolic Equations ◽  
Parabolic Problems ◽  
Renormalized Solutions ◽  
L1 Data ◽  
Nonlinear Parabolic ◽  
Lower Order Terms

In this work, we prove an existence result of renormalized solutions in Orlicz-Sobolev spaces for a class of nonlinear parabolic equations with two lower order terms and L1-data. 

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