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Titlebook: Lectures on Nonlinear Evolution Equations; Initial Value Proble Reinhard Racke Book 19921st edition Springer Fachmedien Wiesbaden 1992 a pr

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楼主: Malicious
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,,-,,-decay estimates for the linear wave equation,For the proof of Theorem 1.1 simple decay properties of solutions to the linear wave equation play an important role (see Chapter 7). The decay rates of ..-norms are typically of polynomial order in JET depending on the space dimension . and on ..
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Linear symmetric hyperbolic systems,Let . = .(.) = (..,...,..)(.,.), t ≥ 0, ϵ ℝ.. ϵ N, and let the formal linear differential operator . be defined by ..
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,Global solutions to wave equations — proofs,We are now able to give a proof of Theorem 1.1, first again for the case .as discussed in the previous chapters.
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https://doi.org/10.1007/978-3-663-10629-6a priori estimates; equation; evolution; global solutions; hyperbolic system; initial value problems; inte
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High energy estimates,, (5.2) with the assumptions (5.3) — (5.6) on the nonlinearity (case α = 1). Without loss of generality for further investigations we assume the constant g. appearing in the local existence Theorem 5.8 to be sufficiently small as it will be needed in the proof of the next theorem.
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