Global existence and finite time blow-up for a class of semilinear pseudo-parabolic equations

作者：Xu, Runzhang^*; Su, Jia

来源：Journal of Functional Analysis, 2013, 264(12): 2732-2763.

DOI：10.1016/j.jfa.2013.03.010

• Semilinear pseudo-parabolic equation
• Global existence
• Finite time blow-up
• Asymptotic behavior
• Comparison principle

In this paper, we study a class of semilinear pseudo-parabolic equations. By introducing a family of potential wells, we prove the invariance of some sets, global existence, nonexistence and asymptotic behavior of solutions with initial energy J(u(0)) <= d. Moreover, we obtain finite time blow-up with high initial energy J(u(0)) > d by comparison principle.

• 出版日期2013-6-15
• 单位哈尔滨工程大学