Wave equations and reaction-diffusion equations with several nonlinear source terms  

作　　者：刘亚成 徐润章 于涛 

机构地区：[1]College of Science,Harbin Engineering University

出　　处：《Applied Mathematics and Mechanics(English Edition)》2007年第9期1209-1218,共10页应用数学和力学（英文版）

基　　金：the National Natural Science Foundation of China(No.10271034);the Basic Research Foundation of Harbin Engineering University(No.HEUF04012)

摘　　要：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 invarianee 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.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 invarianee 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.

关 键 词：wave equations reaction-diffusion equations  potential wells  global existence  nonexistence 

分 类 号：O175.2[理学—数学]