TY - JOUR

T1 - An inverse problem for a nonlinear hyperbolic equation

AU - Romanov, V. G.

AU - Bugueva, T. V.

N1 - This work was performed within the state assignment of the Sobolev Institute of Mathematics of the Siberian Branch of the Russian Academy of Science, project no. FWNF-2022-0009.

PY - 2024/7/26

Y1 - 2024/7/26

N2 - For a second-order hyperbolic equation with inhomogeneity (Formula Presented), a forward and an one-dimensional inverse problems are studied. The inverse problem is devoted to determining the coefficient under heterogeneity. As an additional information, the trace of the derivative with respect to x of the solution to the forward initial-boundary value problem is given at x = 0 on a finite interval. Conditions for the unique solvability of the forward problem are found. For the inverse problem a local existence and uniqueness theorems are established and a stability estimate of its solutions is found.

AB - For a second-order hyperbolic equation with inhomogeneity (Formula Presented), a forward and an one-dimensional inverse problems are studied. The inverse problem is devoted to determining the coefficient under heterogeneity. As an additional information, the trace of the derivative with respect to x of the solution to the forward initial-boundary value problem is given at x = 0 on a finite interval. Conditions for the unique solvability of the forward problem are found. For the inverse problem a local existence and uniqueness theorems are established and a stability estimate of its solutions is found.

KW - inverse problem

KW - nonlinear equation

KW - stability estimate

KW - uniqueness

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85199415724&origin=inward&txGid=2550e5c0e5eeed745e4408512d4e8e30

UR - https://elibrary.ru/item.asp?id=68769394

UR - https://www.webofscience.com/wos/woscc/full-record/WOS:001272356700009

UR - https://www.mendeley.com/catalogue/bf9c3b79-2051-3b73-90c7-e1a5f3f443c1/

U2 - 10.32523/2306-6172-2024-12-2-134-154

DO - 10.32523/2306-6172-2024-12-2-134-154

M3 - Article

VL - 12

SP - 134

EP - 154

JO - Eurasian Journal of Mathematical and Computer Applications

JF - Eurasian Journal of Mathematical and Computer Applications

SN - 2306-6172

IS - 2

M1 - 9

ER -