Global existence for a coupled wave system related to the Strauss conjecture

Jason Metcalfe; David Spencer

doi:10.3934/cpaa.2018032

Article Contents

2018, Volume 17, Issue 2: 593-604. Doi: 10.3934/cpaa.2018032

This issue Previous Article On the nonlinear convection-diffusion-reaction problem in a thin domain with a weak boundary absorption Next Article Positive solutions for Kirchhoff-Schrödinger-Poisson systems with general nonlinearity

Global existence for a coupled wave system related to the Strauss conjecture

Jason Metcalfe^1, and
David Spencer^2, ,

1.
Department of Mathematics, University of North Carolina -Chapel Hill, Chapel Hill, NC, 27599-3250, USA
2.
UCLA Mathematics Department, Box 951555, Los Angeles, CA, 90095-1555, USA

* Corresponding author: David Spencer
* Corresponding author: David Spencer

Received: March 2017

Revised: August 2017

Published: July 2018

The first author was supported in part by NSF grant DMS-1054289. The second author was supported in part by a Summer Undergraduate Research Fellowship (SURF) through the University of North Carolina, and the results contained herein were developed as a part of his Undergraduate Honors Thesis.

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Abstract

A coupled system of semilinear wave equations is considered, and a small data global existence result related to the Strauss conjecture is proved. Previous results have shown that one of the powers may be reduced below the critical power for the Strauss conjecture provided the other power sufficiently exceeds such. The stability of such results under asymptotically flat perturbations of the space-time where an integrated local energy decay estimate is available is established.

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Mathematics Subject Classification: Primary:35L70, 35L05;Secondary:58J45.

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