Journal
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
Volume 27, Issue 1, Pages 101-124Publisher
JOHN WILEY & SONS LTD
DOI: 10.1002/mma.446
Keywords
wave equations; weak dissipation; a priori estimates
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We consider the Cauchy problem for the weakly dissipative wave equation squareupsilon + mu/1+t upsilont = 0, x is an element of R-n, t greater than or equal to 0 I + t parameterized by mu > 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 mu and that mu = 2 is critical. Copyright (C) 2004 John Wiley Sons, Ltd.
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