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On a class of nonlinear parabolic equations with natural growth in non-reflexive Musielak spaces | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 96، دوره 12، شماره 1، مرداد 2021، صفحه 1207-1233 اصل مقاله (533.08 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.21148.2235 | ||
| نویسندگان | ||
| Bourahma Mohamed* 1؛ Deval Sidi Mohamed1؛ Bennouna Jaouad1؛ Abdelmoujib Benkirane2 | ||
| 1Laboratory of mathematical analysis and applications (LAMA), Department of mathematics, Faculty of Sciences Dhar el Mahraz, Sidi Mohamed Ben Abdellah University, PB 1796 Fez, Morocco | ||
| 2Departement of Mathematics Faculte of Sciences SIdi Mohamed Ben Abdellah University Dhar Mahraz Fez Morocco | ||
| تاریخ دریافت: 29 مرداد 1399، تاریخ بازنگری: 19 دی 1399، تاریخ پذیرش: 16 اسفند 1399 | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Parabolic problems؛ Musielak spaces؛ Renormalized solutions؛ natural growth | ||
| مراجع | ||
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