Fundamental solution for a degenerate hyperbolic operator in Gevrey classes

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...

A Fundamental Solution of N. Zeilon's Operator

P. Marcolongo ON THE SOLVABILITY IN GEVREY CLASSES OF A LINEAR OPERATOR IN TWO VARIABLES

We show non solvability results in Gevrey spaces Gs for a linear partial differential operator with a single real characteristic of constant multiplicity m, m ≥ 3, provided s > m/(m−2)+δ, where δ > 0 depends on the order of the degeneracy of a suitable lower order term. In particular, δ → 0 as the order of the degeneracy tends to +∞.

On some fixed points properties and convergence theorems for a Banach operator in hyperbolic spaces

In this paper, we prove some fixed points properties and demiclosedness principle for a Banach operator in uniformly convex hyperbolic spaces. We further propose an iterative scheme for approximating a fixed point of a Banach operator and establish some strong and $Delta$-convergence theorems for such operator in the frame work of uniformly convex hyperbolic spaces. The results obtained in this...

Discrete Fundamental Solution Preconditioning for Hyperbolic Systems of PDE

We present a new preconditioner for the iterative solution of linear systems of equations arising from discretizations of systems of first order partial differential equations (PDEs) on structured grids. Such systems occur in many important applications, including compressible fluid flow and electormagnetic wave propagation. The preconditioner is a truncated convolution operator, with a kernel ...