Scattering for critical wave equations with variable coefficients

Shi Zhuo Looi; Mihai Tohaneanu

doi:10.1017/S0013091521000158

Scattering for critical wave equations with variable coefficients

Shi Zhuo Looi, Mihai Tohaneanu

Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We prove that solutions to the quintic semilinear wave equation with variable coefficients in scatter to a solution to the corresponding linear wave equation. The coefficients are small and decay as, but are allowed to be time dependent. The proof uses local energy decay estimates to establish the decay of the norm of the solution as.

Original language	English
Pages (from-to)	298-316
Number of pages	19
Journal	Proceedings of the Edinburgh Mathematical Society
Volume	64
Issue number	2
DOIs	https://doi.org/10.1017/S0013091521000158
State	Published - May 2021

Bibliographical note

Publisher Copyright:
Copyright © The Author(s), 2021. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society.

Keywords

defocusing
hyperbolic equation
nonlinear wave equation
power-type non-linearity
power-type nonlinearity
scattering
semilinear wave equations
variable coefficients

ASJC Scopus subject areas

General Mathematics

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10.1017/S0013091521000158

Cite this

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title = "Scattering for critical wave equations with variable coefficients",

abstract = "We prove that solutions to the quintic semilinear wave equation with variable coefficients in scatter to a solution to the corresponding linear wave equation. The coefficients are small and decay as, but are allowed to be time dependent. The proof uses local energy decay estimates to establish the decay of the norm of the solution as.",

keywords = "defocusing, hyperbolic equation, nonlinear wave equation, power-type non-linearity, power-type nonlinearity, scattering, semilinear wave equations, variable coefficients",

author = "Looi, {Shi Zhuo} and Mihai Tohaneanu",

note = "Publisher Copyright: Copyright {\textcopyright} The Author(s), 2021. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society.",

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language = "English",

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T1 - Scattering for critical wave equations with variable coefficients

AU - Looi, Shi Zhuo

AU - Tohaneanu, Mihai

PY - 2021/5

Y1 - 2021/5

N2 - We prove that solutions to the quintic semilinear wave equation with variable coefficients in scatter to a solution to the corresponding linear wave equation. The coefficients are small and decay as, but are allowed to be time dependent. The proof uses local energy decay estimates to establish the decay of the norm of the solution as.

AB - We prove that solutions to the quintic semilinear wave equation with variable coefficients in scatter to a solution to the corresponding linear wave equation. The coefficients are small and decay as, but are allowed to be time dependent. The proof uses local energy decay estimates to establish the decay of the norm of the solution as.

KW - defocusing

KW - hyperbolic equation

KW - nonlinear wave equation

KW - power-type non-linearity

KW - power-type nonlinearity

KW - scattering

KW - semilinear wave equations

KW - variable coefficients

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DO - 10.1017/S0013091521000158

M3 - Article

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VL - 64

SP - 298

EP - 316

JO - Proceedings of the Edinburgh Mathematical Society

JF - Proceedings of the Edinburgh Mathematical Society

IS - 2

ER -

Scattering for critical wave equations with variable coefficients

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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