scholarly journals Existence result for nonlinear parabolic problems with L1-data

2010 ◽  
Vol 37 (4) ◽  
pp. 483-508
Author(s):  
Abderrahmane El Hachimi ◽  
Jaouad Igbida ◽  
Ahmed Jamea
Keyword(s):  
Existence Result ◽  
Parabolic Problems ◽  
Nonlinear Parabolic Problems ◽  
L1 Data ◽  
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 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. 

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

Renormalised solutions of nonlinear parabolic problems with L1 data: existence and uniqueness

1997 ◽  
Vol 127 (6) ◽  
pp. 1137-1152 ◽  
Author(s):  
D. Blanchard ◽  
F. Murat
Keyword(s):  
Nonlinear Problem ◽  
Existence And Uniqueness ◽  
Dual Space ◽  
Continuous Operator ◽  
Parabolic Problems ◽  
Nonlinear Parabolic Problems ◽  
Test Function ◽  
L1 Data ◽  
Nonlinear Parabolic ◽  
Image Position

In this paper we prove the existence and uniqueness of a renormalised solution of the nonlinear problemwhere the data f and u0 belong to L1(Ω × (0, T)) and L1 (Ω), and where the function a:(0, T) × Ω × ℝN → ℝN is monotone (but not necessarily strictly monotone) and defines a bounded coercive continuous operator from the space into its dual space. The renormalised solution is an element of C0 ([ 0, T] L1 (Ω)) such that its truncates TK(u) belong to withthis solution satisfies the equation formally obtained by using in the equation the test function S(u)φ, where φ belongs to and where S belongs to C∞(ℝ) with

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