A class of non-analytic functions for the global solvability of Kirchhoff equation

2014/09/02 by Fumihiko Hirosawa, Hirosawa, Fumihiko
Engineering · Mathematics · #35L15 #35L70 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Stability and Controllability of Differential Equations #math.AP #msc:35L15 #msc:35L70

paper · pdf · doi:10.48550/arxiv.1409.0623

arxiv created 2014/09/02 · openalex publication_date 2014/09/02 · arxiv updated 2014/09/03 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We consider the global solvability to the Cauchy problem of Kirchhoff equation with generalized classes of Manfrin's class. Manfrin's class is a subclass of Sobolev space, but we shall extend this class as a subclass of the ultradifferentiable class, and we succeed to prove the global solvability of Kirchhoff equation with large data in wider classes from the previous works.

Related

• The global solvability of the Kirchhoff equation with Sobolev data
• On the Gevrey well-posedness of the Kirchhoff equation
• Almost Global Solutions of Kirchhoff Equation
• Almost global existence for Kirchhoff equations around global solutions
• Global asymptotic behavior of solutions to a class of Kirchhoff equations