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Blow‐up of solutions to semilinear strongly damped wave equations with different nonlinear terms in an exterior domain
Mathematical Methods in the Applied Sciences ( IF 2.9 ) Pub Date : 2021-01-18 , DOI: 10.1002/mma.7223
Wenhui Chen 1 , Ahmad Z. Fino 2
Affiliation  

In this paper, we consider the initial boundary value problem in an exterior domain for semilinear strongly damped wave equations with power nonlinear term of the derivative‐type |ut|q or the mixed‐type |u|p + |ut|q, where p, q > 1. On one hand, employing the Banach fixed‐point theorem, we prove local (in‐time) existence of mild solutions. On the other hand, under some conditions for initial data and the exponents of power nonlinear terms, the blow‐up results are derived by applying the test function method.

中文翻译:

在外部域中具有不同非线性项的半线性强阻尼波动方程解的爆破

在本文中,我们考虑了初始边界值问题与衍生型的功率非线性项半线性强阻尼波动方程外域| ü Ť | q或混合类型| ü | p  + | ü Ť | q,其中p,  q  > 1。一方面,利用Banach不动点定理,我们证明了温和解的局部(实时)存在。另一方面,在某些条件下,对于初始数据和幂非线性项的指数,应用测试函数方法可以得出爆破结果。
更新日期:2021-01-18
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