Entropy solutions for a nonlinear parabolic problems with lower order term in Orlicz spaces

2016 ◽  
Vol 7 (1) ◽  
pp. 47-76 ◽  
Author(s):  
M. Mabdaoui ◽  
H. Moussa ◽  
M. Rhoudaf
Keyword(s):  
Lower Order ◽  
Order Term ◽  
Orlicz Spaces ◽  
Lower Order Term ◽  
Entropy Solutions ◽  
Parabolic Problems ◽  
Nonlinear Parabolic Problems ◽  
Nonlinear Parabolic

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

Renormalized solutions to nonlinear parabolic problems in generalized Musielak–Orlicz spaces

2015 ◽  
Vol 129 ◽  
pp. 1-36 ◽  
Author(s):  
P. Gwiazda ◽  
P. Wittbold ◽  
A. Wróblewska-Kamińska ◽  
A. Zimmermann
Keyword(s):  
Orlicz Spaces ◽  
Parabolic Problems ◽  
Renormalized Solutions ◽  
Nonlinear Parabolic Problems ◽  
Nonlinear Parabolic

scholarly journals Obstacle parabolic equations in non-reflexive Musielak-Orlicz spaces

2018 ◽  
Vol 4 (2) ◽  
pp. 189-206
Author(s):  
Ahmed Aberqi ◽  
Jaouad Bennouna ◽  
Mhamed Elmassoudi
Keyword(s):  
Parabolic Equation ◽  
Vector Field ◽  
Lower Order ◽  
Parabolic Equations ◽  
General Class ◽  
Order Term ◽  
Orlicz Spaces ◽  
Penalization Method ◽  
Nonlinear Parabolic ◽  
Monotone Vector Field

AbstractWe prove existence of entropy solutions to general class of unilateral nonlinear parabolic equation in inhomogeneous Musielak-Orlicz spaces avoiding ceorcivity restrictions on the second lower order term. Namely, we consider$$\left\{ \matrix{ \matrix{ {u \ge \psi } \hfill & {{\rm{in}}} \hfill & {{Q_T},} \hfill \cr } \hfill \cr {{\partial b(x,u)} \over {\partial t}} - div\left( {a\left( {x,t,u,\nabla u} \right)} \right) = f + div\left( {g\left( {x,t,u} \right)} \right) \in {L^1}\left( {{Q_T}} \right). \hfill \cr} \right.$$The growths of the monotone vector field a(x, t, u, ᐁu) and the non-coercive vector field g(x, t, u) are controlled by a generalized nonhomogeneous N- function M (see (3.3)-(3.6)). The approach does not require any particular type of growth of M (neither Δ2 nor ᐁ2). The proof is based on penalization method.

scholarly journals Existence of solutions for some strongly nonlinear parabolic problems involving lower order terms in divergence form in Musielak-Orlicz spaces

2019 ◽  
Vol 38 (6) ◽  
pp. 99-126
Author(s):  
Abdeslam Talha ◽  
Abdelmoujib Benkirane
Keyword(s):  
Lower Order ◽  
Parabolic Equations ◽  
Existence Of Solutions ◽  
Orlicz Spaces ◽  
Nonlinear Parabolic Equations ◽  
Parabolic Problems ◽  
Strongly Nonlinear ◽  
L1 Data ◽  
Nonlinear Parabolic ◽  
Lower Order Terms

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

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