Wave equations and reaction-diffusion equations with several nonlinear source terms
Wave equations and reaction-diffusion equations with several nonlinear source terms
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DOI：
10.3934/dcdsb.2007.7.171
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发表时间：
2006-10
影响因子：
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通讯作者：
Ya-cheng Liu;Runzhang Xu;Tao Yu
中科院分区：
文献类型：
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作者：
Ya-cheng Liu;Runzhang Xu;Tao Yu
利用势阱方法研究了有界区域上具有多个非线性源项的波动方程和反应扩散方程的初边值问题。通过引入势威尔斯族，得到了这类问题在流动下某些集合的不变性和解的真空隔离性。进而给出了解的整体存在和不存在的门槛结果.最后讨论了临界初始条件下的问题。
The initial boundary value problem of wave equations and reaction-diffusion equations with several nonlinear source terms in a bounded domain is studied by potential well method. The invariance of some sets under the flow of these problems and the vacuum isolation of solutions are obtained by introducing a family of potential wells. Then the threshold result of global existence and nonexistence of solutions are given. Finally, the problem with critical initial conditions are discussed.