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Jason Metcalfe

Publications and source records attributed to Jason Metcalfe.

40 records · Page 3Linked to original sources
arXiv2004

Global existence of quasilinear, nonrelativistic wave equations satisfying the null condition

We prove global existence of solutions to multiple speed, Dirichlet-wave equations with quadratic nonlinearities satisfying the null condition in the exterior of compact obstacles. This extends the result of our previous paper by allowing general higher order terms. In the currect setting, these terms are much more difficult to handle than for the free wave equation, and we do so using an analog of a pointwise estimate due to Kubota and Yokoyama.

math.AP↗
arXiv2003

Hyperbolic trapped rays and global existence of quasilinear wave equations

We prove global existence for quasilinear wave equations outside of a wide class of obstacles. The obstacles may contain trapped hyperbolic rays as long as there is local exponential energy decay for the associated linear wave equation. Thus, we can handle all non-trapping obstacles. We are also able to handle non-diagonal systems satisfying the appropriate null condition.

math.AP↗
arXiv2003

Global existence for semilinear wave equations exterior to nontrapping obstacles

In this paper, we show global existence, in spatial dimensions greater than or equal to four, for semilinear wave equations with quadratic nonlinearities exterior to a nontrapping obstacle. This extends the previous work of Shibata-Tsutsumi and Hayashi. Shibata-Tsutsumi showed the result for spatial dimensions greater than or equal to 6, and Hayashi proved the result exterior to a ball.

math.AP↗