Thursday, 14 January 2010

Damped wave equation in the subcritical case

aDepartment of Mathematics, Graduate School of Science, Osaka University, Osaka, Toyonaka 560-0043, JapanbDepartamento de Ciencias Básicas, Instituto Tecnológico de Morelia, Morelia CP 58120, Michoacán, Mexico
cInstituto de Matemáticas, Unam Campus Morelia, AP 61-3 (Xangari), Morelia CP 58089, Michoacán, Mexico

Received 22 July 2003; 
revised 31 March 2004. 
Available online 12 August 2004.


We study large time asymptotics of small solutions to the Cauchy problem for the one dimensional nonlinear damped wave equation

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in the sub critical case σset membership, variant(2-var epsilon3,2). We assume that the initial data v0,(1+∂x)-1v1set membership, variantLL1,a, aset membership, variant(0,1) where

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Also we suppose that the mean value of initial data

Then there exists a positive value var epsilon such that the Cauchy problem (1) has a unique global solution v(t,x)set membership, variantC([0,∞);LL1,a), satisfying the following time decay estimate:

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for large t>0, here 2-var epsilon3<σ<2.
Keywords: Damped wave equation; Subcritical nonlinearity; Asymptotic expansion; Large time behavior



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