Entropy solutions to parabolic equations in Musielak framework involving non coercivity term in divergence form

Title:

Entropy solutions to parabolic equations in Musielak framework involving non coercivity term in divergence form

Creator:

Elemine Vall, Mohamed Saad Bouh, Ahmed, Ahmed, Touzani, Abdelfattah, and Benkirane, Abdelmoujib

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:5ee87219-6bdc-4af8-9da1-4cf1e64c7a44
uuid:5ee87219-6bdc-4af8-9da1-4cf1e64c7a44
doi:10.21136/MB.2017.0087-16

Subject:

inhomogeneous Musielak-Orlicz-Sobolev space, parabolic problems, and Galerkin method

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

We prove the existence of solutions to nonlinear parabolic problems of the following type: ∂b(u)⁄ ∂t + A(u) = f + div(Θ(x;t; u)) in Q, u(x;t) = 0 on ∂Ω × [0; T ], b(u)(t = 0) = b(u0) on Ω, where b : ℝ → ℝ is a strictly increasing function of class C 1 , the term A(u) = −div (a(x, t, u, ∇u)) is an operator of Leray-Lions type which satisfies the classical Leray-Lions assumptions of Musielak type, Θ: Ω × [0; T ] × ℝ → ℝ is a Carathéodory, noncoercive function which satisfies the following condition: sup |s|≤k |Θ(·, ·, s)| ∈ Eψ(Q) for all k > 0, where ψ is the Musielak complementary function of Θ, and the second term f belongs to L 1 (Q).

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

225-249

Source:

Mathematica bohemica | 2018 Volume:143 | Number:3

Harvested from:

CDK

Metadata only:

false