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Global solutions for a nonlinear degenerate nonlocal problem | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 2، دوره 14، شماره 10، دی 2023، صفحه 9-17 اصل مقاله (387.08 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2023.26510.3338 | ||
| نویسنده | ||
| Eugenio Cabanillas Lapa* | ||
| Instituto de Investigacion, FCM-UNMSM, Av. Venezuela S/N, Lima, Peru | ||
| تاریخ دریافت: 02 فروردین 1401، تاریخ بازنگری: 21 مرداد 1402، تاریخ پذیرش: 24 مرداد 1402 | ||
| چکیده | ||
| In this paper, we consider the existence and asymptotic behavior of solutions to the following new nonlocal problem $$ u_{tt}- M\Big(\displaystyle \int_{\Omega}|\nabla u|^{2}\, dx\Big)\triangle u + \delta u_{t}= |u|^{\rho-2}u\hspace{1.0cm} \text{in}\ \Omega \times ]0,\infty[, $$ where \begin{equation*} M(s)=\begin{cases} a-bs &\text{for } \ \, s \in [0,\frac{a}{b}[,\\ 0, &\text{for } s \in [\frac{a}{b}, +\infty[. \end{cases} \end{equation*} We first state a local existence theorem. Next, if the initial energy is appropriately small, by using Tartar's method and the decay rate of the energy, we derive the global existence theorem. As a biproduct, we also obtain the exponential decay property of the global solution. | ||
| کلیدواژه‌ها | ||
| global solutions؛ degenerate nonlocal problem؛ asymptotic behavior | ||
| مراجع | ||
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