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Asymptotic behavior of solutions to the generalized cubic double dispersion equation in one space dimension

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  • We study the initial value problem for the generalized cubic double dispersion equation in one space dimension. We establish a nonlinear approximation result to our global solutions that was obtained in [6]. Moreover, we show that as time tends to infinity, the solution approaches the superposition of nonlinear diffusion waves which are given explicitly in terms of the self-similar solution of the viscous Burgers equation. The proof is based on the semigroup argument combined with the analysis of wave decomposition.
    Mathematics Subject Classification: Primary: 35L30, 35L76, 35B40; Secondary: 35C06.

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