Blow up for small-amplitude semilinear wave equations with mixed nonlinearities on asymptotically Euclidean manifolds
Blow up for small-amplitude semilinear wave equations with mixed nonlinearities on asymptotically Euclidean manifolds
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DOI：
10.1016/j.jde.2020.06.032
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发表时间：
2019-12
影响因子：
2.4
通讯作者：
Mengyun Liu;Chengbo Wang
中科院分区：
文献类型：
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作者：
Mengyun Liu;Chengbo Wang
本文研究了具有混合非线性项c1的小振幅半线性波动方程解的有限时间爆破问题以及寿命的上界估计|u t| p+ c 2| u| q，在渐近欧氏流形上，它与Strauss猜想和Alfressey猜想有关.在某些情况下，我们得到的存在性结果，其中的寿命的下限同意的上限，以秩序。此外，我们的结果适用于半线性阻尼波方程，当耗散项的系数是可积的（没有符号条件）和空间无关。
In this work, we investigate the problem of finite time blow up as well as the upper bound estimates of lifespan for solutions to small-amplitude semilinear wave equations with mixed nonlinearities c 1| u t| p+ c 2| u| q, posed on asymptotically Euclidean manifolds, which is related to both the Strauss conjecture and the Glassey conjecture. In some cases, we obtain existence results, where the lower bound of the lifespan agrees with the upper bound in order. In addition, our results apply for semilinear damped wave equations, when the coefficient of the dissipation term is integrable (without sign condition) and space-independent.