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Generalized p(x)-elliptic system with non physical data
Farah Balaadich,Elhoussine Azroul
Keywords:p(x)-Laplacian systems, Variable exponents, Weak solutions, Young measures
Abstract:
      This paper is concerned with 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 $W^{1,p(x)}_0(\Omega;\R^m)$.