Papers by Mhamed Elmassoudi
Rendiconti del Circolo Matematico di Palermo, May 16, 2024
Filomat, 2023
In the current paper, we investigate the existence and regularity of weak solutions to a class of... more In the current paper, we investigate the existence and regularity of weak solutions to a class of non-uniformly elliptic equations with degenerate coercivity and non-polynomial growth. The model case is given as follows: An L ∞ -estimate of solutions is also obtained for an L 1 -datum f.
Boletín de la Sociedad Matemática Mexicana
AIP Conference Proceedings, 2019
In this work, we shall be concerned with the existence result to the nonlinear elliptic equations... more In this work, we shall be concerned with the existence result to the nonlinear elliptic equations −div(a(x,u,∇u))+Φ(x,u))+g(x,u,∇u)=0 in the setting of Orlicz spaces. The results obtained are prove...
Journal of applied analysis and computation, 2024
Journal de Mathématiques Pures et Appliquées, 2003
In this paper we prove the existence of a renormalized solution for a class of non coercive nonli... more In this paper we prove the existence of a renormalized solution for a class of non coercive nonlinear equations whose prototype is: − p u + b(x)|∇u| λ = µ in Ω, u = 0 o n ∂Ω, where Ω is a bounded open subset of R N , N 2, p is the so called p-Laplace operator, 1 < p < N, µ is a Radon measure with bounded variation on Ω, 0 λ p − 1 and b belongs to the Lorentz space L N,1 (Ω). 2003 Published by Éditions scientifiques et médicales Elsevier SAS. Résumé Dans cet article nous démontrons l'existence d'une solution renormalisée pour une classe d'équations non linéaires non coercives dont le prototype est : − p u + b(x)|∇u| λ = µ dans Ω,
Gulf Journal of Mathematics
In this paper we will prove the existence of solutions of the unilateral problem Au - div Φ(x,u) ... more In this paper we will prove the existence of solutions of the unilateral problem Au - div Φ(x,u) + H(x, u, ∇ u) = μ in Musielak spaces, where A is a Leray-Lions operator defined on D(A) ⊂ W01 LM (Ω), μ ∈ L(Ω) + W-1 EM'(Ω), where M and M' are two complementary Musielak-Orlicz functions and both the first and the second lower terms Φ and H satisfies only the growth condition and u ≥ ζ where ζ is a measurable function.
Boundary Value Problems
This manuscript proves the existence of a nonnegative, nontrivial solution to a class of double-p... more This manuscript proves the existence of a nonnegative, nontrivial solution to a class of double-phase problems involving potential functions and logarithmic nonlinearity in the setting of Sobolev space on complete manifolds. Some applications are also being investigated. The arguments are based on the Nehari manifold and some variational techniques.
Our aim in this paper is to discuss the existence of renormalized solutions of the following syst... more Our aim in this paper is to discuss the existence of renormalized solutions of the following systems: ∂bi(x, ui) ∂t −div(a(x, t, ui,∇ui))−φi(x, t, ui))+fi(x, u1, u2) = 0 i=1,2. where the function bi(x, ui) verifies some regularity conditions, the term ( a(x, t, ui,∇ui) ) is a generalized Leray-Lions operator and φi is a Carathéodory function assumed satisfy only a growth condition. The source term fi(t, u1, u2) belongs to L1(Ω× (0, T )) .
Our aim in this paper is to discuss the existence of renormalized solutions of the following syst... more Our aim in this paper is to discuss the existence of renormalized solutions of the following systems: ∂bi(x, ui) ∂t −div(a(x, t, ui,∇ui))−φi(x, t, ui))+fi(x, u1, u2) = 0 i=1,2. where the function bi(x, ui) verifies some regularity conditions, the term ( a(x, t, ui,∇ui) ) is a generalized Leray-Lions operator and φi is a Carathéodory function assumed satisfy only a growth condition. The source term fi(t, u1, u2) belongs to L1(Ω× (0, T )) .
Ukrains’kyi Matematychnyi Zhurnal, 2021
UDC 517.5 In this article, we study the existence result of the unilateral problemwhere is a Lera... more UDC 517.5 In this article, we study the existence result of the unilateral problemwhere is a Leray–Lions operator defined on Sobolev–Orlicz space where and are two complementary -functions, the first and the second lower terms and satisfies only the growth condition and any sign condition is assumed and where is a measurable function.
Mathematical Modeling and Computing, 2021
In this paper, a class of nonlinear evolution equations with damping arising in fluid dynamics an... more In this paper, a class of nonlinear evolution equations with damping arising in fluid dynamics and rheology is studied. The nonlinear term is monotone and possesses a convex potential but exhibits non-standard growth. The appropriate functional framework for such equations is the modularly Museilak–spaces. The existence and uniqueness of a weak solution are proved using an approximation approach by combining an internal approximation with the backward Euler scheme, also a priori error estimate for the temporal semi-discretization is given.
Advances in Operator Theory, 2022
Advances in Science, Technology and Engineering Systems Journal
= 0, where the function b i (x, u i) verifies some regularity conditions, the term a(x, t, u i , ... more = 0, where the function b i (x, u i) verifies some regularity conditions, the term a(x, t, u i , ∇u i) is a generalized Leray-Lions operator and φ i is a Carathéodory function assumed to be continuous on u i and satisfy only a growth condition. The source term f i (t, u 1 , u 2) belongs to L 1 (Ω × (0, T)).
Boletim da Sociedade Paranaense de Matemática
This paper, is devoted to an existence result of entropy unilateral solutions for the nonlinear p... more 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 $L^{1}(\Omega)$.
Moroccan Journal of Pure and Applied Analysis
We prove existence of entropy solutions to general class of unilateral nonlinear parabolic equati... more We 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.
Advances in Science, Technology and Engineering Systems Journal
We prove an existence result of entropy solutions for the nonlinear parabolic problems: ∂b(x,u) ∂... more We prove an existence result of entropy solutions for the nonlinear parabolic problems: ∂b(x,u) ∂t +A(u)−div(Φ(x, t, u))+H(x, t, u, ∇u) = f , and A(u) = −div(a(x, t, u, ∇u)) is a Leary-Lions operator defined on the inhomogeneous Musielak-Orlicz space, the term Φ(x, t, u) is a Crathéodory function assumed to be continuous on u and satisfy only the growth condition Φ(x, t, u) ≤ c(x, t)M −1 M(x, α 0 u), prescribed by Musielak-Orlicz functions M and M which inhomogeneous and not satisfy ∆ 2-condition, H(x, t, u, ∇u) is a Crathéodory function not satisfies neither the sign condition or coercivity and f ∈ L 1 (Q T).
Journal of Differential …, 2001
... 反应扩散, post-grouting. Existence and Uniqueness of a Renormalized Solution for a Fairly General... more ... 反应扩散, post-grouting. Existence and Uniqueness of a Renormalized Solution for a Fairly General Class of Nonlinear Parabolic Problems. DOI：, 作者 ：, Dominique Blanchard；Francois Murat；Hicham Redwane. 期刊 ：, Journal of Differential Equations SCI. 年，卷(期) ：, 2001, 177 ...
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Papers by Mhamed Elmassoudi