Fundamental Solutions for Hyperbolic Operators with Variable Coefficients

Abstract

In this article we describe the novel method to construct fundamental solutions for operators with variable coefficients. That method was introduced in "A note on the fundamental solution for the Tricomi-type equation in the hyperbolic domain"(J. Differential Equations,206(2004)227--252) to study the Tricomi-type equation. More precisely, the new integral operator is suggested which transforms the family of the fundamental solutions of the Cauchy problem for the equation with the constant coefficients to the fundamental solutions for the operators with variable coefficients.

References in corpus (2)

• Huygens' principle and anomalously small radiation tails
• Regularity of Solutions to Second-Order Integral Functionals in Variational Calculus

Cited by in corpus (5)

• Huygens' Principle for the Klein-Gordon equation in the de Sitter spacetime
• A note on the nonexistence of global solutions to the semilinear wave equation with nonlinearity of derivative-type in the generalized Einstein-de Sitter spacetime
• Integral representation formulae for the solution of a wave equation with time-dependent damping and mass in the scale-invariant case
• On a semilinear wave equation in anti-de Sitter spacetime: the critical case
• Integral transform approach to solving Klein-Gordon equation with variable coefficients