ASYMPTOTIC GEVREY CLASSES AND THE CAUCHY PROBLEM FOR NON-STRICTLY HYPERBOLIC LINEAR DIFFERENTIAL EQUATIONS.

Abstract

The notion of asymptotic Gevrey classes alpha, alpha > 1 is introduced. These classes are related to but distinct from the Gevrey classes used by J. Leray and Y. Ohya in connection with the Cauchy problem for a nonstrictly hyperbolic equation defined on a strip X in R sub (l+1), l = or > 1. A characterization of an asymptotic Gevrey class alpha is given in terms of conditions on the determining sequence of the class. To this end, the work of S. Mandelbrojt on classes of infinitely differentiable functions is extended to strips X and to the norms associated with these strips. Asymptotic Gevrey classes are then applied to a study of the Cauchy problem for a non-strictly hyperbolic linear differential equation on X. It is proved that if the coefficients of the differential operator, the non-homogeneous term, and the Cauchy data belong to certain asymptotic Gevrey classes alpha, then a solution exists on X which belongs to an appropriate Gevrey class alpha. (Author)

Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1969
Accession Number
AD0693628

Entities

People

  • Edward Newberger

Organizations

  • Indiana University Bloomington

Tags

DTIC Thesaurus Topics

  • Boundary Value Problems
  • Cauchy Problem
  • Coefficients
  • Differential Equations
  • Equations
  • Linear Differential Equations
  • Mathematical Analysis
  • Mathematics
  • Nonlinear Differential Equations

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Linear Algebra
  • Statistical inference.