Abstract
We study the Cauchy problem for the nonlinear damped wave equation and establish the large data local well-posedness and small data global well-posedness with slowly decaying initial data. We also prove that the asymptotic profile of the global solution is given by a solution of the corresponding parabolic problem, which shows that the solution of the damped wave equation has the diffusion phenomena. Moreover, we show blow-up of solution and give the estimate of the lifespan for a subcritical nonlinearity. In particular, we determine the critical exponent for any space dimension.
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Ikeda, M., Inui, T. & Wakasugi, Y. The Cauchy problem for the nonlinear damped wave equation with slowly decaying data. Nonlinear Differ. Equ. Appl. 24, 10 (2017). https://doi.org/10.1007/s00030-017-0434-1
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DOI: https://doi.org/10.1007/s00030-017-0434-1