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Quasilinear parabolic problems in the Lebsgue-Sobolev space with variable exponent and $L^1$ data | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 10، دوره 15، شماره 10، دی 2024، صفحه 117-130 اصل مقاله (496.63 K) | ||
| نوع مقاله: Review articles | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2023.30528.4423 | ||
| نویسندگان | ||
| Souilah Fairouz1، 2؛ Maouni Messaoud* 2؛ Kamel Slimani* 2 | ||
| 1University 20th August 1955, Skikda, Algeria | ||
| 2Laboratory of Applied Mathematics and History and Didactics of Maths "LAMAHIS", Algeria | ||
| تاریخ دریافت: 11 اردیبهشت 1402، تاریخ بازنگری: 25 مرداد 1402، تاریخ پذیرش: 27 مرداد 1402 | ||
| چکیده | ||
| In this work, we study the existence of an initial boundary problem of a quasilinear parabolic problem with variable exponent and $ L ^{1} $-data of the type \begin{equation*} \left\{ \begin{array}{ll} (b(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=f(x,t,u) \text{ } & \text{in}\hspace{0.5cm}Q=\Omega \times ]0,T[, \\ u=0 & \text{on}\hspace{0.5cm}\Sigma =\partial \Omega \times ]0,T[, \\ b(u)(t=0)=b(u_{0}) & \text{in}\hspace{0.5cm}\Omega , \end{array} \right. \end{equation*} where $ \lambda>0$ and $ T $ is positive constant. The main contribution of our work is to prove the existence of a renormalized solution. The functional setting involves Lebesgue– Sobolev spaces with variable exponents. | ||
| کلیدواژهها | ||
| Quasilinear parabolic problems؛ variable exponent؛ truncations؛ renormalized solutions؛ L1 data | ||
| مراجع | ||
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