Abstract
We 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.
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Acknowledgements
The author would like to express deep appreciation to Professor Satoshi Masaki, Professor Yoshihiro Ueda, and, Professor Yuta Wakasugi for encouragement. Moreover, he also thanks to Professor Vladimir Georgiev, Professor Tohru Ozawa, Professor Michael Ruzhansky, and, Professor Jens Wirth for inviting me the session “Harmonic Analysis and Partial Differential Equations” in 12th ISAAC Congress. The author is supported by JSPS KAKENHI Grant-in-Aid for Early-Career Scientists JP18K13444.
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Inui, T. (2020). Remark on Asymptotic Order for the Energy Critical Nonlinear Damped Wave Equation to the Linear Heat Equation via the Strichartz Estimates. In: Georgiev, V., Ozawa, T., Ruzhansky, M., Wirth, J. (eds) Advances in Harmonic Analysis and Partial Differential Equations. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-58215-9_10
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DOI: https://doi.org/10.1007/978-3-030-58215-9_10
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