Remark on Asymptotic Order for the Energy Critical Nonlinear Damped Wave Equation to the Linear Heat Equation via the Strichartz Estimates

Takahisa Inui

doi:10.1007/978-3-030-58215-9_10

Remark on Asymptotic Order for the Energy Critical Nonlinear Damped Wave Equation to the Linear Heat Equation via the Strichartz Estimates

Takahisa Inui

https://doi.org/10.1007/978-3-030-58215-9_10

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Publication Date: Jan 1, 2020

Affiliation: Osaka University

#Damped Wave Equation #Strichartz Estimates + Show 8 more

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Abstract

AbstractWe consider the damped wave equation with the energy critical power type nonlinearity. It is known that the global solution with a finite space-time norm decays to 0 as time goes to infinity. In the present paper, we give the asymptotic order that the solution goes to a solution of the linear heat equation.KeywordsDamped wave equationAsymptotic behaviorStrichartz estimate

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