Work

Green’s Function for the Cauchy Problem to the Dissipative Linear Evolution Equation of Arbitrary Order

Year: 2025

Type: article

Abstract: This work addresses the Cauchy problem for a linear equation with a first-order time derivative t and an arbitrary-order spatial derivative x. This equation is a generalization of the linear heat equation of the second order in the case of arbitrary order with respect to spatial variable. The considered linear equation arises from the linearization of the Burgers hierarchy of equations. The Cauchy problem to a linear equation can be solved using the Green function method. The Green function is explicitly constructed for the case of dissipative and dispersive equations and is expressed in terms of generalized hypergeometric functions. The general formulas obtained for representing Green’s function are new. A discussion of specific cases of the equation is also provided.

Source: Mathematics

DOI: 10.3390/math13182966

Authors: Daniil R. Nifontov, Nikolay A. Kudryashov

Institution: National Research Nuclear University MEPhI

Language: English

Topic: Differential Equations and Boundary Problems

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funder: Ministry of Science and Higher Education of the Russian Federation