Damped wave equation with a critical nonlinearity

Authors:
Nakao Hayashi, Elena I. Kaikina and Pavel I. Naumkin

Journal:
Trans. Amer. Math. Soc. **358** (2006), 1165-1185

MSC (2000):
Primary 35Q55; Secondary 35B40

DOI:
https://doi.org/10.1090/S0002-9947-05-03818-3

Published electronically:
April 22, 2005

MathSciNet review:
2187649

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Abstract | References | Similar Articles | Additional Information

Abstract: We study large time asymptotics of small solutions to the Cauchy problem for nonlinear damped wave equations with a critical nonlinearity

where and space dimensions . Assume that the initial data

where weighted Sobolev spaces are

Also we suppose that

where

Then we prove that there exists a positive such that the Cauchy problem above has a unique global solution satisfying the time decay property

for all where

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Additional Information

**Nakao Hayashi**

Affiliation:
Department of Mathematics, Graduate School of Science, Osaka University, Osaka, Toyonaka, 560-0043, Japan

Email:
nhayashi@math.wani.osaka-u.ac.jp

**Elena I. Kaikina**

Affiliation:
Departamento de Ciencias Básicas, Instituto Tecnológico de Morelia, Morelia CP 58120, Michoacán, Mexico

Email:
ekaikina@matmor.unam.mx

**Pavel I. Naumkin**

Affiliation:
Instituto de Matemáticas, UNAM Campus Morelia, AP 61-3 (Xangari), Morelia CP 58089, Michoacán, Mexico

Email:
pavelni@matmor.unam.mx

DOI:
https://doi.org/10.1090/S0002-9947-05-03818-3

Keywords:
Damped wave equation,
large time asymptotics

Received by editor(s):
April 1, 2003

Received by editor(s) in revised form:
April 22, 2004

Published electronically:
April 22, 2005

Additional Notes:
The second and the third authors were supported in part by CONACYT

Article copyright:
© Copyright 2005
American Mathematical Society