GENERALIZED P(X)-ELLIPTIC SYSTEM WITH NONLINEAR PHYSICAL DATA

Elhoussine Azroul; Farah Balaadich

doi:10.11948/20190309

2020 Volume 10 Issue 5

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Elhoussine Azroul, Farah Balaadich. GENERALIZED P(X)-ELLIPTIC SYSTEM WITH NONLINEAR PHYSICAL DATA[J]. Journal of Applied Analysis & Computation, 2020, 10(5): 1995-2007. doi: 10.11948/20190309

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Elhoussine Azroul, Farah Balaadich. GENERALIZED P(X)-ELLIPTIC SYSTEM WITH NONLINEAR PHYSICAL DATA[J]. Journal of Applied Analysis & Computation, 2020, 10(5): 1995-2007. doi: 10.11948/20190309

GENERALIZED P(X)-ELLIPTIC SYSTEM WITH NONLINEAR PHYSICAL DATA

Elhoussine Azroul¹,
Farah Balaadich^1, ,

1.
Department of Mathematics, Faculty of Sciences Dhar El Mehraz, B.P. 1796 Atlas, Fez-Morocco

Corresponding author: Email: balaadich.edp@gmail.com(F. Balaadich)

Abstract

Abstract

This paper considers the following Dirichlet problem of the form $ -\text{div}\, \big(\Phi(Du-\Theta(u)\big) = v(x)+f(x, u)+\text{div}\, \big(g(x, u)\big), $ which corresponds to a diffusion problem with a source $ v $ in moving and dissolving substance, the motion is described by $ g $ and the dissolution by $ f $. By the theory of Young measure we will prove the existence result in variable exponent Sobolev spaces $ W^{1, p(x)}_0(\Omega; \mathbb{R}^m) $.
- p(x)-Laplacian systems /
- variable exponents /
- weak solutions /
- young measures
MSC: 35Jxx, 46E30, 35D30, 28Axx

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References

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