Research output: Contribution to journal › Article › peer-review
An inverse problem for a nonlinear hyperbolic equation. / Romanov, V. G.; Bugueva, T. V.
In: Eurasian Journal of Mathematical and Computer Applications, Vol. 12, No. 2, 9, 26.07.2024, p. 134-154.Research output: Contribution to journal › Article › peer-review
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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 -
ID: 61172564