Global Existence for High Dimensional Quasilinear Wave Equations Exterior to Star-shaped Obstacles
نویسندگان
چکیده
1. Introduction. The purpose of this article is to study long time existence for high dimensional quasilinear wave equations exterior to star-shaped obstacles. In particular, we seek to prove exterior domain analogs of the four dimensional results of [5] where the nonlinearity is permitted to depend on the solution not just its first and second derivatives. Previous proofs in exterior domains omitted this dependence as it did not mesh well with the energy methods in use. The main estimates used in the proof are the variable coefficient localized energy estimate of [12] as well as a constant coefficient variant of this estimate which was developed in [1], [3], and [4].
منابع مشابه
Long-Time Existence of Quasilinear Wave Equations Exterior to Star-Shaped Obstacles via Energy Methods
We establish long-time existence results for quasilinear wave equations in the exterior of star-shaped obstacles. To do so, we prove an analogue of the mixed-norm estimates of Keel, Smith, and Sogge for the perturbed wave equation. The arguments that are presented rely only upon the invariance of the wave operator under translations and spatial rotations.
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