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- W3168982014 abstract "We consider a singular limit problem from the damped wave equation with a power type nonlinearity to the corresponding heat equation. We call our singular limit problem non-delay limit. Our proofs are based on the argument for non-relativistic limit from the nonlinear Klein-Gordon equation to the nonlinear Schr{o}dinger equation by the second author, Nakanishi, and Ozawa (2002), Nakanishi (2002), and Masmoudi and Nakanishi (2002). We can obtain better results for the non-delay limit problem than that for the non-relativistic limit problem due to the dissipation property. More precisely, we get the better convergence rate of the $L^2$-norm and we also obtain the global-in-time uniform convergence of the non-delay limit in the $L^2$-supercritical case." @default.
- W3168982014 created "2021-06-22" @default.
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- W3168982014 date "2021-06-06" @default.
- W3168982014 modified "2023-09-27" @default.
- W3168982014 title "Non-delay limit in the energy space from the nonlinear damped wave equation to the nonlinear heat equation" @default.
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- W3168982014 doi "https://doi.org/10.48550/arxiv.2106.03030" @default.
- W3168982014 hasPublicationYear "2021" @default.
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