Hokkaido Mathematical Journal

Hoshiga Akira,

The existence of the global solutions to semilinear wave equations with a class of cubic nonlinearities in 2-dimensional space.

Hokkaido Mathematical Journal, 37 (2008) pp.669-688




This paper deals with the Cauchy problem of the semilinear wave equation with a small initial data in 2-dimensional space. When the nonlinearity is cubic, we can not expect the global existence of smooth solutions, in general. However, Godin [1] showed that if the nonlinearity has the null-form, the solution exists globally. In this paper, we will show the global solvability for the other type of nonlinearities which does not have null-form.

MSC(Secondary)35L15, 35L70
Uncontrolled Keywordssemilinear wave equation, null-condition, global solvability.