Asymptotic limits for mildly degenerate Kirchhoff equations

2011/05/26 by Marina Ghisi, Ghisi Marina, Marina, Ghisi
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Dynamics and Pattern Formation #Quantum chaos and dynamical systems #Stability and Controllability of Differential Equations #math.AP

paper · pdf · doi:10.48550/arxiv.1105.5358

arxiv created 2011/05/26 · openalex publication_date 2011/05/26 · arxiv updated 2011/05/27 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

We study the asymptotic behavior of the solutions of the mildly degenerate Kirchhoff equation with a dissipative term. We obtain a new estimate on second-in-time derivative of the solution. Moreover we renormalize the solution in such a way that the renormalization as a no zero limit as t goes to infinity. Finally we calculate explicitly the norm of this limit and we prove that it does not depend on the initial data.

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