Remarks on global solutions of dissipative wave equations with exponential nonlinear terms

Makoto Nakamura

doi:10.3934/cpaa.2015.14.1533

Article Contents

2015, Volume 14, Issue 4: 1533-1545. Doi: 10.3934/cpaa.2015.14.1533

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Remarks on global solutions of dissipative wave equations with exponential nonlinear terms

Makoto Nakamura^1,

1.
Faculty of Science, Yamagata University, Kojirakawa-machi 1-4-12, Yamagata 990-8560

Received: June 30, 2013

Revised: February 28, 2014

Published: June 2015

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Abstract

The Cauchy problem for dissipative wave equations with exponential type nonlinear terms is considered in the energy space in two spatial dimensions. The nonlinear terms have a singularity at the origin, and global solutions are shown based on the Gagliardo-Nirenberg type inequality.

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Mathematics Subject Classification: Primary: 35L70.

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