Advanced Studies in Pure Mathematics

Diffusion phenomenon of solutions to the Cauchy problem for the damped wave equation

Kenji Nishihara

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Abstract

We survey the recent results for the damped wave equations and obtain the critical exponent for the semilinear problem. Those results are based on the diffusion phenomenon of the damped wave equation.

Article information

Source
Nonlinear Dynamics in Partial Differential Equations, S. Ei, S. Kawashima, M. Kimura and T. Mizumachi, eds. (Tokyo: Mathematical Society of Japan, 2015), 125-136

Dates
Received: 9 January 2012
First available in Project Euclid: 30 October 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1540934208

Digital Object Identifier
doi:10.2969/aspm/06410125

Mathematical Reviews number (MathSciNet)
MR3381197

Zentralblatt MATH identifier
1347.35172

Subjects
Primary: 35B33: Critical exponents 35B40: Asymptotic behavior of solutions 35L71: Semilinear second-order hyperbolic equations

Keywords
Diffusion phenomenon damped wave equation asymptotic behavior

Citation

Nishihara, Kenji. Diffusion phenomenon of solutions to the Cauchy problem for the damped wave equation. Nonlinear Dynamics in Partial Differential Equations, 125--136, Mathematical Society of Japan, Tokyo, Japan, 2015. doi:10.2969/aspm/06410125. https://projecteuclid.org/euclid.aspm/1540934208


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