Nonlinear parabolic inequalities in Lebesgue-Sobolev spaces with variable exponent

被引：8

作者：

Bennouna J. ^{[1
]}

El hamdaoui B. ^{[1
]}

Mekkour M. ^{[2
]}

Redwane H. ^{[3
]}

机构：

[1] Département de Mathématiques, Laboratoire LAMA, Faculté des Sciences Dhar-Mahrez, Université Sidi Mohammed Ben Abdellah, B.P 1796, Atlas Fès

[2] Laboratoire d’Informatique, Automatique et Optoélectronique, Faculté Polydisciplinaire de Mathmatiques, Université Sidi Mohamed Ben Abdellah, Taza

[3] Faculté des Sciences Juridiques, Economiques et Sociales, Université Hassan 1, Settat

来源：

Ricerche di Matematica | 2016年 / 65卷 / 1期

关键词：

Entropy solutions; Parabolic problem; Penalized equations; Sobolev space; Variable exponent;

D O I：

10.1007/s11587-016-0255-2

中图分类号：

学科分类号：

摘要：

We give an existence result of the obstacle parabolic problem: $begin{aligned} left{ begin{array}{ll} uge psi &{} text{ a.e. } text{ in } Omega times (0,T)\ displaystyle frac{partial b(x,u)}{partial t} -div(a(x,t,u,nabla u))+div(phi (x,t,u)) =f &{} text{ in } Omega times (0,T).\ end{array} right. end{aligned}${u≥ψa.e.inΩ×(0,T)∂b(x,u)∂t-div(a(x,t,u,∇u))+div(ϕ(x,t,u))=finΩ×(0,T).The main contribution of our work is to prove the existence of an entropy solution without the coercivity condition on ϕ. The second term f belongs to L1(Ω × (0 , T)) and b(. , u0) ∈ L1(Ω). The proof is based on the penalization methods. © 2016, Università degli Studi di Napoli Federico II"."

引用

页码：93 / 125

页数：32

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