Potential well method for initial boundary value problem of the generalized double dispersion equations

作者：Liu Yacheng^*; Xu Runzhang

来源：Communications on Pure and Applied Analysis, 2008, 7(1): 63-81.

DOI：10.3934/cpaa.2008.7.63

• generalized double dispersion equation
• initial boundary value
• potential wells
• global existence
• nonexistence

In this paper we study the initial boundary value problem of the generalized double dispersion equations u(tt) - u(xx) - u(xxtt) + u(xxxx) = f(u)(xx), where f(u) include convex function as a special case. By introducing a family of potential wells we first prove the invariance of some sets and vacuum isolating of solutions, then we obtain a threshold result of global existence and nonexistence of solutions. Finally we discuss the global existence of solutions for problem with critical initial condition.

• 出版日期2008-1
• 单位哈尔滨工程大学