Integral Transform Approach to Generalized Tricomi Equations
Karen Yagdjian
TL;DR
This paper introduces an integral transform method that simplifies solving generalized Tricomi equations by relating them to simpler equations, enabling unified analysis of various related PDEs in different spacetime models.
Contribution
The paper develops a new integral transform approach to solve generalized Tricomi equations, extending its application to multiple PDEs in mathematical physics.
Findings
Transform allows deriving solutions from simpler equations.
Unified approach for Tricomi, Gellerstedt, wave, and Klein-Gordon equations.
Applicable to equations in Einstein-de Sitter, de Sitter, and anti-de Sitter spacetimes.
Abstract
We present some integral transform that allows to obtain solutions of the generalized Tricomi equation from solutions of a simpler equation. We used in [13,14],[41]-[46] the particular version of this transform in order to investigate in a unified way several equations such as the linear and semilinear Tricomi equations, Gellerstedt equation, the wave equation in Einstein-de Sitter spacetime, the wave and the Klein-Gordon equations in the de Sitter and anti-de Sitter spacetimes.
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