The existence of the global solutions to semilinear wave equations with a class of cubic nonlinearities in 2-dimensional space
HOSHIGA, Akira
Hokkaido Math. J., Tome 37 (2008) no. 4, p. 669-688 / Harvested from Project Euclid
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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.
Publié le : 2008-11-15
Classification:  semilinear wave equation,  null-condition,  global solvability,  35L05,  35L15,  35L70 
@article{1249046363,
     author = {HOSHIGA, Akira},
     title = {The existence of the global solutions to semilinear wave equations with a class of cubic nonlinearities in 2-dimensional space},
     journal = {Hokkaido Math. J.},
     volume = {37},
     number = {4},
     year = {2008},
     pages = { 669-688},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1249046363}
}

HOSHIGA, Akira. The existence of the global solutions to semilinear wave equations with a class of cubic nonlinearities in 2-dimensional space. Hokkaido Math. J., Tome 37 (2008) no. 4, pp.  669-688. http://gdmltest.u-ga.fr/item/1249046363/