Lifespan estimates for semilinear wave equations with space dependent damping and potential
Lifespan estimates for semilinear wave equations with space dependent damping and potential
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DOI：
10.1007/s00526-022-02388-0
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发表时间：
2021-02
影响因子：
2.1
通讯作者：
Ning-An Lai;Mengyun Liu;Ziheng Tu;Chengbo Wang
中科院分区：
文献类型：
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作者：
Ning-An Lai;Mengyun Liu;Ziheng Tu;Chengbo Wang
在这项工作中，我们调查的影响，一般阻尼和潜在的条款上的爆破和寿命估计的能量型半线性波动方程。空间相关的阻尼和潜在的功能被假定为临界或短程，球对称扰动。利用所谓的检验函数方法得到了爆破结果和寿命估计的上界。关键成分是构造特殊的正解的线性对偶问题所需的渐近行为，这是减少，反过来，构造解决某些椭圆形的“特征值”问题。
In this work, we investigate the influence of general damping and potential terms on the blow-up and lifespan estimates for energy solutions to power-type semilinear wave equations. The space-dependent damping and potential functions are assumed to be critical or short range, spherically symmetric perturbation. The blow up results and the upper bound of lifespan estimates are obtained by the so-called test function method. The key ingredient is to construct special positive solutions to the linear dual problem with the desired asymptotic behavior, which is reduced, in turn, to constructing solutions to certain elliptic “eigenvalue” problems.