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Volume 10, Number 5, 2020, Pages 1995-2007                                                                DOI:10.11948/20190309
Generalized p(x)-elliptic system with nonlinear physical data
Elhoussine Azroul,Farah Balaadich
Keywords:p(x)-Laplacian systems, variable exponents, weak solutions, young measures.
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 $W^{1,p(x)}_0(\Omega;\R^m)$.
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