# American Institute of Mathematical Sciences

March  2012, 11(2): 547-556. doi: 10.3934/cpaa.2012.11.547

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

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

Received  September 2010 Revised  February 2011 Published  October 2011

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.
Citation: Jason Metcalfe, Jacob Perry. Global solutions to quasilinear wave equations in homogeneous waveguides with Neumann boundary conditions. Communications on Pure & Applied Analysis, 2012, 11 (2) : 547-556. doi: 10.3934/cpaa.2012.11.547
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