Classical solution of the Cauchy problem for a semilinear wave equation with a Dirac potential
https://doi.org/10.29235/1561-8323-2025-69-1-7-12
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.
About the Authors
V. I. Korzyuk
Institute of Mathematics of the National Academy of Sciences of Belarus
Belarus
Belarus
Korzyuk Viktor I. – Academician, D. Sc. (Physics and Ma thematics), Professor
11, Surganov Str., 220072, Minsk
J. V. Rudzko
Institute of Mathematics of the National Academy of Sciences of Belarus
Belarus
Belarus
Rudzko Jan V. – Master (Mathematics and Computer Sciences), Postgraduate Student
11, Surganov Str., 220072, Minsk
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