Work

Classical solution of the initial-value problem for a one-dimensional quasilinear wave equation

Year: 2023

Type: article

Abstract: For a one-dimensional mildly quasilinear wave equation given in the upper half-plane, we consider the Cauchy problem. The solution is constructed by the method of characteristics in an implicit analytical form as a solution of some integro-differential equation. The solvability of this equation, as well the smoothness of its solution, is studied. For the problem in question, the uniqueness of the solution is proved and the conditions under which its classical solution exists are established. When given data is not enough smooth a mild solution is constructed.

Source: Doklady of the National Academy of Sciences of Belarus

DOI: 10.29235/1561-8323-2023-67-1-14-19

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

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

OpenAlex ID: W4323544656

FWCI: 2.622

Cites: 15

Cited by: 12

Related to: 10