On a class of nonlinear parabolic equations with natural growth in non-reflexive Musielak spaces
نویسندگان
1 Departement of Mathematics Faculte of Sciences SIdi Mohamed Ben Abdellah University Dhar Mahraz Fez Morocco
2 Laboratory of mathematical analysis and applications (LAMA), Department of mathematics, Faculty of Sciences Dhar el Mahraz, Sidi Mohamed Ben Abdellah University, PB 1796 Fez, Morocco
3 Laboratory of mathematical analysis and applications (LAMA), Department of mathematics, Faculty of Sciences Dhar el Mahraz, Sidi Mohamed Ben Abdellah University, PB 1796 Fez, Morocco
4 Laboratory of mathematical analysis and applications (LAMA), Department of mathematics, Faculty of Sciences Dhar el Mahraz, Sidi Mohamed Ben Abdellah University, PB 1796 Fez, Morocco
doi
10.22075/ijnaa.2021.21148.2235چکیده
An existence result of renormalized solutions for nonlinear parabolic Cauchy-Dirichlet problems whose model$$\left\{\begin{array}{ll}\displaystyle\frac{\partial b(x,u)}{\partial t}-\mbox{div}\>\mathcal{A}(x,t,u,\nabla u)-\mbox{div}\>\Phi(x,t,u)=f &\mbox{ in }\Omega\times (0,T)\\b(x,u)(t=0)=b(x,u_0) & \mbox{ in } \Omega\\u=0 &\mbox{ on } \partial\Omega\times (0,T).\end{array}\right.$$is given in the non reflexive Musielak spaces, where $b(x,\cdot)$ is a strictly increasing $C^1$-function for every $x\in\Omega$ with $b(x,0)=0$, the lower order term $\Phi$ is a non coercive Carath\'{e}odory function satisfying only a natural growth condition described by the appropriate Musielak function $\varphi$ and $f$ is an integrable data.
