Fourth order wave equations with nonlinear strain and source terms
Fourth order wave equations with nonlinear strain and source terms
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DOI：
10.1016/j.jmaa.2006.09.010
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发表时间：
2007-07
影响因子：
1.3
通讯作者：
Ya-cheng Liu;Runzhang Xu
中科院分区：
文献类型：
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作者：
Ya-cheng Liu;Runzhang Xu
本文研究了具有非线性应变和源项的四阶波动方程的初边值问题。首先，我们引入了一族势井，并证明了某些集合的不变性和解的真空隔离性。然后我们得到了整体存在和不存在的一个阈值结果。最后讨论了临界初始条件为I(U0)⩾0，E(0)=d的问题解的整体存在性，推广和改进了Esquivel-Avila的结果。
In this paper we study the initial boundary value problem for fourth order wave equations with nonlinear strain and source terms. First we introduce a family of potential wells and prove the invariance of some sets and vacuum isolating of solutions. Then we obtain a threshold result of global existence and nonexistence. Finally we discuss the global existence of solutions for the problem with critical initial condition I(u0)⩾0, E(0)=d. So the Esquivel-Avila's results are generalized and improved.