位势井在3个非线性源项波动方程中的应用  

Potential Well and Its Applications to Wave Equations with Three Nonlinear Source Terms

作　　者：李宝平[1] 帅鲲[2] 蒲志林[3] 

机构地区：[1]电子科技大学成都学院,四川成都611731 [2]四川师范大学成都学院,四川成都611745 [3]四川师范大学数学与软件科学学院,四川成都610066

出　　处：《四川师范大学学报（自然科学版）》2014年第2期152-156,共5页Journal of Sichuan Normal University（Natural Science）

基　　金：四川省基础科学基金(2010JY0057)资助项目

摘　　要：为了研究一类半线性波动方程的初边值问题解的适定性,引进一种新的位势井方法,通过新构建的变分法来计算位势井深度并定义新的位势井,利用新位势井方法得到了解的不变集合,新位势井方法结合紧致性方法得到了具有3个非线性源项波动方程的初边值问题解的整体存在性,结合凸性方法得到了解的有限时间爆破.主要定理揭示了解的初始值对整体适定性的影响,同时这种新的位势井方法使得应用位势井理论处理问题的机制更加清晰,从而进一步丰富和发展了位势井理论.In order to study the we11-posedness of solutions to an initial boundary value problem for a class of semilinear wave equa- tions, a new potential well method is introducced. By constructing a new variational problem the depth of potential well is calculated and a new potential well is defined. The invariant sets of solutions are obtained by new potential well method and convergence method. The global existence and finite time blow-up of three nonlinear source terms of solutions to initial boundary value problem for wave e- quations are also obtained. The main theorems of the thesis reveal the fact that initial value of solutions influences the global well-pos- edness of solutions. This new potential well method makes the internal and external mechanisms that we use potential well theory to process problem much more clear. Consequently, this work further enriches and develoos the existin~ notential well.theorv.

关 键 词：非线性波动方程 位势井 存在性 有限时间爆破 

分 类 号：O175.2[理学—数学]