MATHEMATICS

On the absence, non-uniqueness, and blow-up of classical solutions of mixed problems for the telegraph equation with a nonlinear potential

V. I. Korzyuk^ab, J. V. Rudzko<sup>b

a</sup> Belarusian State University, Minsk
^b Institute of Mathematics of the National Academy of Sciences of Belarus, Minsk

Abstract: For the telegraph equation with a nonlinear potential given in the first quadrant, we consider the first and the second mixed problem, for which we study issues related to the absence, non-uniqueness, and blow-up of classical solutions.

Keywords: semilinear wave equation, mixed problem, classical solution, absence of solution, non-uniqueness of solution, blow-up of solution, method of characteristics, energy methods, matching conditions.

UDC: 517.956.35

Received: 20.12.2023

Language: English

DOI: 10.54341/20778708_2024_2_59_73