https://doi.org/10.1140/epjp/s13360-020-00568-5
Regular Article
Global existence and blowup of solutions for a class of nonlinear wave equations with linear pseudo-differential operator
1
College of Automation, Harbin Engineering University, 150001, Harbin, Heilongjiang, People’s Republic of China
2
College of Mathematical Sciences, Harbin Engineering University, 150001, Harbin, Heilongjiang, People’s Republic of China
Received:
21
February
2020
Accepted:
29
June
2020
Published online:
15
July
2020
This paper pays attention to the Cauchy problem for a class of nonlinear wave equations with linear pseudo-differential operator. In the framework of variational arguments, the existence and nonexistence of global solution to this problem are derived when the total initial energy is less than or equal to the mountain pass level. Further, a finite-time blowup result for arbitrarily high initial energy is established.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020