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Local well-posedness and blow-up of solution for a higher-order wave equation with viscoelastic term and variable-exponent | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 10، دوره 14، شماره 4، تیر 2023، صفحه 111-124 اصل مقاله (1.68 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2023.29383.4149 | ||
| نویسندگان | ||
| Boughamsa Wissem* 1؛ Ouaoua Amar2 | ||
| 1Department of Mathematics, Laboratory of Applied Mathematics and History and Didactics of Mathematics (LAMAHIS), University of 20 August 1955, Skikda, Algeria | ||
| 2Department of Sciences and Technology, Laboratory of Applied Mathematics and History and Didactics of Mathematics (LAMAHIS), University of 20 August 1955, Skikda, Algeria | ||
| تاریخ دریافت: 02 دی 1401، تاریخ بازنگری: 26 بهمن 1401، تاریخ پذیرش: 26 بهمن 1401 | ||
| چکیده | ||
| We investigate in this paper a value problem related to the following nonlinear higher-order wave equation $$ \eta_{tt}+\left( -\Delta\right) ^{m}\eta-% %TCIMACRO{\dint \limits_{0}^{t}}% %BeginExpansion {\displaystyle\int\limits_{0}^{t}} %EndExpansion g\left( t-s\right) \left( -\Delta\right) ^{m}\eta\left( s\right) ds+\eta_{t}=\left\vert \eta\right\vert ^{p\left( x\right) -2}\eta. $$ Firstly, we prove the existence and uniqueness of the local solution under suitable conditions for the relaxation function $g$ and viable-exponent $p\left( .\right) $, using a method, which is a mixture of the Faedo-Galarkin and Banach fixed point theorem, and prove also the solution blows up in finite time. Finally, we give a two-dimensional numerical example to illustrate the blow-up result. | ||
| کلیدواژه‌ها | ||
| Higher-order equation؛ wave equation؛ variable-exponent؛ local solution؛ blow up | ||
| مراجع | ||
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