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Local energy decay and the vector field method. (English) Zbl 1469.35041

Giga, Yoshikazu (ed.) et al., The role of metrics in the theory of partial differential equations. Proceedings of the 11th Mathematical Society of Japan, Seasonal Institute (MSJ-SI), Nagoya University, Japan, July 2–13 2018. Tokyo: Mathematical Society of Japan. Adv. Stud. Pure Math. 85, 369-378 (2021).
Summary: We discuss recent work concerning stability of solutions to linear and nonlinear wave equations on asymptotically flat space times. This is joint work with Jason Metcalfe, Jesus Oliver, and Daniel Tataru.
For the entire collection see [Zbl 1462.35005].

MSC:

35B40 Asymptotic behavior of solutions to PDEs
35L15 Initial value problems for second-order hyperbolic equations
35L71 Second-order semilinear hyperbolic equations
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