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- W2071706553 abstract "We study the long time behavior of small solutions to the nonlinear damped wave equationεuττ+uτ=(a(ξ) uξ)ξ+N(u, uξ, uτ),ξ∈R,τ⩾0, whereεis a positive, not necessarily small parameter. We assume that the diffusion coefficienta(ξ) converges to positive limitsa±asξ→±∞, and that the nonlinearity N(u, uξ, uτ) vanishes sufficiently fast asu→0. Introducing scaling variables and using various energy estimates, we compute an asymptotic expansion of the solutionu(ξ, τ) in powers ofτ−1/2asτ→+∞, and we show that this expansion is entirely determined, up to the second order, by a linear parabolic equation which depends only on the limiting valuesa±. In particular, this implies that the small solutions of the damped wave equation behave for largeτlike those of the parabolic equation obtained by settingε=0." @default.
- W2071706553 created "2016-06-24" @default.
- W2071706553 creator A5045553490 @default.
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- W2071706553 date "1998-11-01" @default.
- W2071706553 modified "2023-10-16" @default.
- W2071706553 title "Scaling Variables and Asymptotic Expansions in Damped Wave Equations" @default.
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- W2071706553 doi "https://doi.org/10.1006/jdeq.1998.3459" @default.
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