This article is cited in 3 papers

The problem of determining the coefficient for power gradient nonlinearity in semilinear wave equation

V. G. Romanov^a, T.V. Bugueva<sup>ba

a</sup> Sobolev Institute of Mathematics SB RAS, pr. Acad. Koptyuga 4, Novosibirsk 630090, Russia
^b Novosibirsk State University, ul. Pirogova 1, Novosibirsk 630090, Russia

Abstract: An one-dimensional inverse problem of determining the coefficient for power gradient nonlinearity in a semilinear wave equation is considered. The existence and uniqueness theorems of the solution of a direct problem are proved. For the inverse problem the local existence theorem is stated and a stability estimate of the solution is found.

Keywords: semilinear wave equation, direct problem, inverse problem, power gradient nonlinearity, existence, stability, uniqueness. .

UDC: 517.956

Received: 12.12.2022
Revised: 14.12.2022
Accepted: 12.01.2023

DOI: 10.33048/SIBJIM.2023.26.210

 English version: Journal of Applied and Industrial Mathematics, 2023, 17:2, 370–384