Gevrey well-posedness of an abstract Cauchy problem of weakly hyperbolic type

Remarks on the Well-Posedness of the Nonlinear Cauchy Problem

We show that hyperbolicity is a necessary condition for the well posedness of the noncharacteristic Cauchy problem for nonlinear partial differential equations. We give conditions on the initial data which are necessary for the existence of solutions and we analyze Hadamard’s instabilities in Sobolev spaces. We also show that genuinely nonlinear equations raise new interesting problems.

Almost global well-posedness of Kirchhoff equation with Gevrey data

Article history: Received 26 November 2016 Accepted after revision 3 April 2017 Available online 18 April 2017 Presented by the Editorial Board The aim of this note is to present the almost global well-posedness result for the Cauchy problem for the Kirchhoff equation with large data in Gevrey spaces. We also briefly discuss the corresponding results in bounded and in exterior domains. © 2017 A...

Inhomogeneous Gevrey Ultradistributions and Cauchy Problem

AMS Mathematics Subject Classification (2000): 46F05, 35E15, 35S05.

Well-posedness for Hyperbolic Problems

Inhomogeneous Two-Parameter Abstract Cauchy Problem