Gevrey-well-posedness for weakly hyperbolic operators with non-regular 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...

Well-posedness for Non-isotropic Degenerate Parabolic-hyperbolic Equations

We develop a well-posedness theory for solutions in L to the Cauchy problem of general degenerate parabolic-hyperbolic equations with non-isotropic nonlinearity. A new notion of entropy and kinetic solutions and a corresponding kinetic formulation are developed which extends the hyperbolic case. The notion of kinetic solutions applies to more general situations than that of entropy solutions; a...

Non-isotropic Gevrey Hypoellipticity for Grushin Operators

We shall determine non-isotropic Gevrey exponents for general Grushin operators based on the results given in the paper [26], where a method to determine isotropic (worst) Gevrey exponents was given. The ideas of the bracket calculus given in the paper [2] and FBI-transformation given in the paper [5] are also useful.

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...