| Issue |
Int. J. Simul. Multidisci. Des. Optim.
Volume 8, 2017
|
|
|---|---|---|
| Article Number | A11 | |
| Number of page(s) | 8 | |
| DOI | https://doi.org/10.1051/smdo/2017004 | |
| Published online | 18 August 2017 | |
Research Article
Study of solutions to a class of certain parabolic systems with variable exponents
1
Research laboratory in Engineering (LRI), University Hassan II of Casablanca, National Higher School of Electricity and Mechanics (ENSEM), BP 8118, Oasis, Morocco
2
Département MIG, Ecole Hassania des Travaux Publics (EHTP), BP 8106, Oasis, Casablanca, Morocco
* e-mail: h.elouardi@ensem.ac.ma
Received:
10
April
2017
Accepted:
22
June
2017
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.
Key words: pi(x)-Laplacian systems / Existence / Uniqueness / Variable exponent / Blow-Up / Semi-discretization
© H. El Ouardi et al., published by EDP Sciences, 2017
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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