Work

Classical solution of the Cauchy problem for a semilinear wave equation with a Dirac potential

Year: 2025

Type: article

Abstract: For a one-dimensional semilinear wave equation with a free term that is a solution value at one given point (a Dirac potential), we consider the Cauchy problem in the upper half-plane. We construct the solution using the method of characteristics in implicit analytical form as a solution of some integral equations. The solvability of these equations, as well the smoothness of their solutions, is studied. For the problem in question, we prove the uniqueness of the solution, and establish the conditions under which its classical solution exists.

Source: Doklady of the National Academy of Sciences of Belarus

DOI: 10.29235/1561-8323-2025-69-1-7-12

Authors: V. I. Korzyuk, J. V. Rudzko

Institutions: National Academy of Sciences of Belarus, Institute of Mathematics

Language: English

Topic: Differential Equations and Boundary Problems

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4408034609

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Cites: 14

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Related to: 10