Solution representations for a wave equation with weak dissipation

Jens Wirth

Type: Article

Publication Date: 2003-12-05

Citations: 137

DOI: https://doi.org/10.1002/mma.446

Abstract

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.

Locations

arXiv (Cornell University) - View - PDF
Mathematical Methods in the Applied Sciences - View - PDF

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Action	Title	Year	Authors
+	Singular Integrals and Differentiability Properties of Functions.	1971	Elias M. Stein
+ PDF Chat	The total energy decay of solutions for the wave equation with a dissipative term	1980	Hiroshi Uesaka
+ PDF Chat	Theory of Bessel potentials. I	1961	N. Aronszajn K. T. Smith
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+ PDF Chat	Estimates for translation invariant operators in Lp spaces	1960	Lars Hörmander
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+ PDF Chat	On the Asymptotic Behavior of Solutions of Semi-linear Wave Equations	1976	Akitaka Matsumura
+ PDF Chat	On spaces of potentials connected with $L^p$ classes	1963	N. Aronszajn P. Szeptycki
+	OnL p?Lp? estimates for the wave-equation	1975	Philip Brenner
+	A Treatise on the Theory of Bessel Functions.	1923	Matthew Porter G. N. Watson