On the metric perurbation for semilinear wave equations
Abstract: In this talk I’d like to revisit a joint work with Professor Katayama in which we dealt with a system of two-components semilinear wave equations. We assume the nonlinearity of one component satisfies null condition, while the other does not, but has a good structure so that the system has a global solution for small initial data. In addition, we can show that the asymptotic behavior is different from the free solution.
Here we extend the result to the case where the propagation speeds depend on the good component which still violate the null condition.