A One-Dimensional Time-Fractional Damped Wave Equation with a Convection Term

被引：0

作者：

Aldawish, Ibtisam ^{[1
]}

Jleli, Mohamed ^{[2
]}

Samet, Bessem ^{[2
]}

机构：

[1] Imam Mohammad Ibn Saud Islamic Univ IMSIU, Coll Sci, Dept Math & Stat, Riyadh 11566, Saudi Arabia

[2] King Saud Univ, Coll Sci, Dept Math, POB 2455, Riyadh 11451, Saudi Arabia

来源：

SYMMETRY-BASEL | 2023年 / 15卷 / 05期

关键词：

damped wave equation; Caputo fractional derivative; convection term; nonexistence; BLOW-UP PHENOMENA; GLOBAL-SOLUTIONS; NONEXISTENCE; SYMMETRIES; REFLECTION;

D O I：

10.3390/sym15051071

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

We investigate a semilinear time-fractional damped wave equation in one dimension, posed in a bounded interval. The considered equation involves a convection term and singular potentials on one extremity of the interval. A Dirichlet boundary condition depending on the time-variable is imposed. Using nonlinear capacity estimates, we establish sufficient conditions for the nonexistence of weak solutions to the considered problem. In particular, when the boundary condition is independent of time, we show the existence of a Fujita-type critical exponent.

引用

页数：17

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