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Space-time decay for solutions of wave equations

✍ Scribed by Irving Segal

Publisher
Elsevier Science
Year
1976
Tongue
English
Weight
321 KB
Volume
22
Category
Article
ISSN
0001-8708

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✦ Synopsis

IN MEMORY OF NORMAN LEVINSON

The LB norm in space-time of a solution of the Klein-Gordon equation in two space-time dimensions is bounded relative to the Lorentz-invariant Hilbert space norm; the L, norms for p > 6 are bounded relative to certain similar larger Hilbert space norms, including the energy norm.

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## Abstract Let __u__ and __v__ be, respectively, the solutions to the Cauchy problems for the dissipative wave equation $$u\_{tt}+u\_t‐\Delta u=0$$\nopagenumbers\end and the heat equation $$v\_t‐\Delta v=0$$\nopagenumbers\end We show that, as $t\rightarrow+\infty$\nopagenumbers\end, the norms