NON-EXISTENCE OF GLOBAL SOLUTIONS TO NONLINEAR WAVE EQUATIONS WITH POSITIVE INITIAL ENERGY

作者：Bilgin Bilgesu A; Kalantarov Varga K^*

来源：Communications on Pure and Applied Analysis, 2018, 17(3): 987-999.

DOI：10.3934/cpaa.2018048

• Global non-existence
• blow up
• differential operator equation
• concavity method
• positive energy

We consider the Cauchy problem for nonlinear abstract wave equations in a Hilbert space. Our main goal is to show that this problem has solutions with arbitrary positive initial energy that blow up in a finite time. The main theorem is proved by employing a result on growth of solutions of abstract nonlinear wave equation and the concavity method. A number of examples of nonlinear wave equations are given. A result on blow up of solutions with arbitrary positive initial energy to the initial boundary value problem for the wave equation under nonlinear boundary conditions is also obtained.

• 出版日期2018-5