Gevrey-well-posedness for weakly hyperbolic operators with Hölder-continuous coefficients

Well-posedness for Hyperbolic 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...

Stii Well{posedness for Hyperbolic Systems with Large Relaxation Terms

The Cauchy problem for linear constant{coeecient hyperbolic systems u t + Au x = (1==)Bu is analyzed. Here (1==)Bu is a large relaxation term, and we are mostly interested in the critical case where B has a non{trivial nullspace. A concept of stii well{posedness is introduced that ensures solution estimates independent of 0 < 1. Under suitable assumptions, we prove convergence of the L 2 {solut...

Well{posedness of Stiff Hyperbolic Systems

The theory of stii well{posedness of initial value problems for hyperbolic systems with large relaxation terms is reviewed. Furthermore, an asymptotic expansion of solutions with respect to the relaxation parameter is presented. Finally, the theory is illustrated with an example and an outlook concerning boundary value problems is given.

D . Calvo GENERALIZED GEVREY CLASSES AND MULTI - QUASI - HYPERBOLIC OPERATORS

In this paper we consider generalized Gevrey classes defined in terms of Newton polyhedra. In such functional frame we prove a theorem of solvability of the Cauchy Problem for a class of partial differential operators, called multi-quasi-hyperbolic. We then give a result of regularity of the solution with respect to the space variables and finally analyze the regularity with respect to the time...