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We give an existence result of the obstacle parabolic equations $$\frac{\partial b(x,u)}{\partial t} -div(a(x,t,u,\nabla u))+div(\phi(x,t,u)) =f\quad \text{in}\ \ Q_T,$$ where $b(x,u)$ is bounded function of $u$, the term $- {\rm div}(a(x,t,u,\nabla u))$ is a Leray-Lions type operator and the function $\phi$ is a nonlinear lower order and satisfy only the growth condition. The second term $f$ belongs to $L^{1}(Q_T)$. The proof of an existence solution is based on the penalization methods.
}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2017.v33.n1.4}, url = {http://global-sci.org/intro/article_detail/ata/4614.html} }We give an existence result of the obstacle parabolic equations $$\frac{\partial b(x,u)}{\partial t} -div(a(x,t,u,\nabla u))+div(\phi(x,t,u)) =f\quad \text{in}\ \ Q_T,$$ where $b(x,u)$ is bounded function of $u$, the term $- {\rm div}(a(x,t,u,\nabla u))$ is a Leray-Lions type operator and the function $\phi$ is a nonlinear lower order and satisfy only the growth condition. The second term $f$ belongs to $L^{1}(Q_T)$. The proof of an existence solution is based on the penalization methods.