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Nonlinear dissipative wave equations with space–time dependent potential

✍ Scribed by Maisa Khader

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
308 KB
Volume
74
Category
Article
ISSN
0362-546X

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We study the asymptotic behavior of solutions of dissipative wave equations with space-time-dependent potential. When the potential is only time-dependent, Fourier analysis is a useful tool to derive sharp decay estimates for solutions. When the potential is only space-dependent, a powerful techniqu

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## Abstract We consider the following semilinear wave equation: equation image for (__t__,__x__) ∈ ℝ~__t__~ × ℝ. We prove that if the potential __V__(__t__,__x__) is a measurable function that satisfies the following decay assumption: ∣__V__(__t__,__x__)∣⩽__C__(1+__t__)(1+∣__x__∣) for a.e. (__t_