2022
DOI: 10.5269/bspm.51207
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The existence of renormalized solution for quasilinear parabolic problem with variable exponents and measure data

Abstract: In this paper, the study of the existence of a renormalized solution for quasilinear parabolicproblem with variable exponents and measure data. The model is: u_{t}-\text{div}(\left\vert \nabla u\right\vert ^{p(x)-2}\nabla u)+\lambda\left\vert u\right\vert ^{p(x)-2}u=\mu\text{ } &\text{in}\hspace{0.5cm}Q=\Omega \times ]0,T[,\\u=0 & \text{on}\hspace{0.5cm}\Sigma =\partial \Omega \times ]0,T[, \\u(.,0)=u_{0}(.) & \text{in}\hspace{0.5cm}\Omega, where $ \lambda>0$ and $ T $ is any positiv… Show more

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