Work

Generalized Monge–Ampère type equation and its multidimensional exact solutions

Year: 2025

Type: article

Abstract: Several variants of the multidimensional generalized Monge–Ampère equation are considered containing, in addition to the determinant of the Hessian matrix, also additional terms depending on the Laplace operator and the gradient of the desired function. It is proposed to construct exact solutions in the form of superposition of quadratic form and solutions of ordinary differential equations generated by the initial partial differential equation. We give a number of examples of exact solutions, both radially symmetric and anisotropic, expressed through combinations of elementary functions.

Source: Vestnik Udmurtskogo Universiteta Matematika Mekhanika Komp yuternye Nauki

DOI: 10.35634/vm250204

Authors: A.A. Kosov, E.I. Semenov

Institutions: Siberian Branch of the Russian Academy of Sciences, Institute for System Dynamics and Control Theory

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4411523719

FWCI: 7.695

Cites:

Cited by: 4

Related to: 10