Study of solutions to a class of certain parabolic systems with variable exponents

In this paper, the authors study an initial and boundary value problem to a system of evolution p(x)-Laplacian systems coupled with general nonlinear terms: ai(x)uit − div(|∇ui|pi(x)−2∇ui) = fi(x, u1, u2), (i = 1, 2). The authors translate the parabolic equation into the elliptic equation by using t...

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Bibliographic Details
Published in:International journal for simulation and multidisciplinary design optimization 2017, Vol.8, p.A11
Main Authors: El Ouardi, Hamid, Ghabbar, Yamna
Format: Article
Language:English
Subjects:
Blow-Up
Boundary value problems
Existence
Nonlinear systems
pi(x)-Laplacian systems
Semi-discretization
Uniqueness
Variable exponent
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Summary:In this paper, the authors study an initial and boundary value problem to a system of evolution p(x)-Laplacian systems coupled with general nonlinear terms: ai(x)uit − div(|∇ui|pi(x)−2∇ui) = fi(x, u1, u2), (i = 1, 2). The authors translate the parabolic equation into the elliptic equation by using the time discretization method, and then the existence and uniqueness solution are obtained. The blow-up results is shown, by using the energy method.
ISSN:1779-627X
1779-6288
1779-6288
DOI:10.1051/smdo/2017004