PDE seminar: A semilinear hyperbolic system violating the nullcondition

2012-12-3 16:30 - 2012-12-3 17:30
Faculty of Science Building #3, Room 309
Soichiro Katayama (Wakayama University)
We consider the Cauchy problem for a two-component
system of semilinear wave equations in three
space dimensions. We treat a certain system which
does not satisfy the null condition of Klainerman, but
whose solution is expected to have bounded energy.
We show the global existence of classical solutions for
small initial data. We also show that one component
will lose its energy, while the other behaves like a
non-trivial free solution in the large time. This talk is
base on a joint work with H. Sunagawa and T. Matoba.