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Blow up of solutions for a r(x)-Laplacian Lam\'{e} equation with variable-exponent nonlinearities and arbitrary initial energy level | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 34، دوره 13، شماره 1، خرداد 2022، صفحه 441-450 اصل مقاله (364.81 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.23671.2578 | ||
| نویسنده | ||
| Mohammad Shahrouzi* | ||
| Department of Mathematics, Jahrom University, Jahrom, Iran | ||
| تاریخ دریافت: 22 خرداد 1400، تاریخ بازنگری: 01 شهریور 1400، تاریخ پذیرش: 24 شهریور 1400 | ||
| چکیده | ||
| In this paper, we consider the nonlinear $r(x)-$Laplacian Lam'{e} equation $$ u_{tt}-\Delta_{e}u-div\big(|\nabla u|^{r(x)-2}\nabla u\big)+|u_{t}|^{m(x)-2}u_{t}=|u|^{p(x)-2}u $$ in a smoothly bounded domain $\Omega\subseteq R^{n},\ n\geq1$, where $r(.),\ m(.)$ and $p(.)$ are continuous and measurable functions. Under suitable conditions on variable exponents and initial data, the blow-up of solutions is proved with negative initial energy as well as positive. | ||
| کلیدواژه‌ها | ||
| blow-up؛ variable-exponent nonlinearities؛ elasticity operator؛ arbitrary initial energy | ||
| مراجع | ||
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