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Solution representations for a wave equation with weak dissipation

✍ Scribed by Jens Wirth

Publisher
John Wiley and Sons
Year
2003
Tongue
English
Weight
187 KB
Volume
27
Category
Article
ISSN
0170-4214

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✦ Synopsis

Abstract

We consider the Cauchy problem for the weakly dissipative wave equation □v+μ/1+t
v~t~=0,
x∈ℝ^n^, t≥0 parameterized by μ>0, and prove a representation theorem for its solutions using the theory of special functions.

This representation is used to obtain L~p~–L~q~ estimates for the solution and for the energy operator corresponding to this Cauchy problem.

Especially for the L~2~ energy estimate we determine the part of the phase space which is responsible for the decay rate. It will be shown that the situation depends strongly on the value of μand that μ=2 is critical. Copyright © 2004 John Wiley & Sons, Ltd.

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