Kirchhoff equations in generalized Gevrey spaces: local existence, global existence, uniqueness

2009/12/18 by Marina Ghisi, Massimo Gobbino, Ghisi, Marina +1 · 1 citation
Engineering · Mathematics · #35L70 #35L80 #35L90 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Spectral Theory in Mathematical Physics #Stability and Controllability of Differential Equations #math.AP #msc:35L70 #msc:35L80 #msc:35L90

paper · pdf · doi:10.48550/arxiv.0912.3690

20 pages, 4 tables, conference paper (7th ISAAC congress, London 2009)

arxiv created 2009/12/18 · openalex publication_date 2009/12/18 · arxiv updated 2010/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note we present some recent results for Kirchhoff equations in generalized Gevrey spaces. We show that these spaces are the natural framework where classical results can be unified and extended. In particular we focus on existence and uniqueness results for initial data whose regularity depends on the continuity modulus of the nonlinear term, both in the strictly hyperbolic case, and in the degenerate hyperbolic case.

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• On the Gevrey well-posedness of the Kirchhoff equation

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