Strongly nonlinear parabolic equations with natural growth terms in Orlicz spaces

2005 ◽  
Vol 60 (1) ◽  
pp. 1-35 ◽  
Author(s):  
A ELMAHI ◽  
D MESKINE
Keyword(s):  
Parabolic Equations ◽  
Orlicz Spaces ◽  
Nonlinear Parabolic Equations ◽  
Natural Growth ◽  
Strongly Nonlinear ◽  
Nonlinear Parabolic ◽  
Natural Growth Terms

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.

Existence of renormalized solutions for strongly nonlinear parabolic problems with measure data

2016 ◽  
Vol 23 (3) ◽  
pp. 303-321 ◽  
Author(s):  
Youssef Akdim ◽  
Abdelmoujib Benkirane ◽  
Mostafa El Moumni ◽  
Hicham Redwane
Keyword(s):  
Growth Condition ◽  
Parabolic Equations ◽  
Nonlinear Parabolic Equations ◽  
Parabolic Problems ◽  
Measure Data ◽  
Renormalized Solution ◽  
Unbounded Function ◽  
Strongly Nonlinear ◽  
Nonlinear Parabolic ◽  
The Right

AbstractWe study the existence result of a renormalized solution for a class of nonlinear parabolic equations of the form${\partial b(x,u)\over\partial t}-\operatorname{div}(a(x,t,u,\nabla u))+g(x,t,u% ,\nabla u)+H(x,t,\nabla u)=\mu\quad\text{in }\Omega\times(0,T),$where the right-hand side belongs to ${L^{1}(Q_{T})+L^{p^{\prime}}(0,T;W^{-1,p^{\prime}}(\Omega))}$ and ${b(x,u)}$ is unbounded function of u, ${{-}\operatorname{div}(a(x,t,u,\nabla u))}$ is a Leray–Lions type operator with growth ${|\nabla u|^{p-1}}$ in ${\nabla u}$. The critical growth condition on g is with respect to ${\nabla u}$ and there is no growth condition with respect to u, while the function ${H(x,t,\nabla u)}$ grows as ${|\nabla u|^{p-1}}$.

scholarly journals Existence of solutions for elliptic equations having natural growth terms in Orlicz spaces

2004 ◽  
Vol 2004 (12) ◽  
pp. 1031-1045 ◽  
Author(s):  
A. Elmahi ◽  
D. Meskine
Keyword(s):  
Elliptic Equation ◽  
Elliptic Equations ◽  
Nonlinear Elliptic Equation ◽  
Existence Result ◽  
Existence Of Solutions ◽  
Orlicz Spaces ◽  
Natural Growth ◽  
Strongly Nonlinear ◽  
Nonlinear Elliptic ◽  
Natural Growth Terms

Existence result for strongly nonlinear elliptic equation with a natural growth condition on the nonlinearity is proved.

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