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Cauchy problem for semilinear wave equation with time-dependent metrics

✍ Scribed by Yavar Kian

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
313 KB
Volume
73
Category
Article
ISSN
0362-546X

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✦ Synopsis

We establish the existence of a weak solution u of the semilinear wave equation

where a(t, x) is equal to 1 outside a compact set with respect to x and a non-linear term f k which satisfies |f k (u)| ≀ C |u | k . For some non-trapping time- periodic perturbations a(t, x), we obtain the long time existence of a solution from little initial data.

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