Global existence and blow-up of solution for the semilinear wave equation with interior and boundary source terms
Global existence and blow-up of solution for the semilinear wave equation with interior and boundary source terms
复制标题
具有内部和边界源项的半线性波动方程解的全局存在性和爆炸
DOI：
10.1186/s13661-019-1129-9
复制
发表时间：
2019-01-23
影响因子：
1.7
通讯作者：
Hu, Qingying
中科院分区：
文献类型：
--
作者：
Zhang, Hongwei;Zhang, Wenxiu;Hu, Qingying
本文研究了具有非线性内源和边界源的半线性波动方程，并考虑了非线性动力边界条件。利用势井方法结合标准的连续引理，在对源项施加适当的假设下，证明了解的整体存在性。此外，对于不稳定集中的某些初始数据，表现出有限时间爆破现象。
This paper is concerned with semilinear wave equations with nonlinear interior and boundary sources and subject to a nonlinear dynamical boundary condition. By using the potential well method combined with a standard continuous argument, under appropriate assumptions imposed on the source term, we establish global existence of solutions. Moreover, for certain initial data in the unstable set, the finite time blow-up phenomenon is exhibited.