Global solutions to quasilinear wave equations in homogeneous waveguides withNeumann boundary conditions

Jason Metcalfe; Jacob Perry

doi:10.3934/cpaa.2012.11.547

Article Contents

2012, Volume 11, Issue 2: 547-556. Doi: 10.3934/cpaa.2012.11.547

This issue Previous Article Nonradial positive solutions for a biharmonic critical growth problem Next Article On the constants in a Kato inequality for the Euler and Navier-Stokes equations

Global solutions to quasilinear wave equations in homogeneous waveguides with Neumann boundary conditions

Jason Metcalfe^1, and
Jacob Perry^1,

1.
Department of Mathematics, University of North Carolina, Chapel Hill, NC 27599-3250

Received: August 31, 2010

Revised: January 31, 2011

Published: February 2012

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Abstract

This article focuses on proving global existence for quasilinear wave equations with small initial data in homogeneous waveguides with infinite base of dimensions $n\geq 4$. The key estimate is a localized energy estimate for a perturbed wave equation.

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Mathematics Subject Classification: Primary: 35L70, 35L20.

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References

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