位势井及其对具异号源项波动方程的应用  

Potential Well and its Applications to Wave Equations with Source Terms of Different Signs

作　　者：徐润章[1] 沈继红[1] 刘亚成[1] 

机构地区：[1]哈尔滨工程大学理学院,哈尔滨150001

出　　处：《工程数学学报》2007年第5期931-934,共4页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(10271034);哈尔滨工程大学基础研究基金(HEUFP05032);黑龙江省教育厅科学技术研究项目(10551254);哈尔滨工程大学创新基金.

摘　　要：本文研究具有两个异号非线性源项的波动方程的初边值问题。应用位势井方法,解决了不具正定能量情况下问题整体解的存在性问题。证明了对于非线性项的指数在一定条件下,问题存在整体弱解。从而拓展了已知结果。The initial boundary value problem of wave equations with two nonlinear source terms of different signs is considered. The global existence of solutions without positive energy is established. It is proven that the indices of the nonlinear terms this problem admits a global weak solution under certain conditions. Some known results are extended.

关 键 词：半线性波动方程 整体解 存在性 位势井 

分 类 号：O175.26[理学—数学]