TY - JOUR

T1 - An one-dimensional inverse problem for the wave 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 - 2024/10/10

Y1 - 2024/10/10

N2 - For the wave equation with inhomogeneity σ(x)umt + q(x)up a forward and an one-dimensional inverse problems are studied. Here m > 1 and p > 1 are real numbers. The forward problem is considered in the domain x > 0, t > 0 with zero initial data and Dirichlet boundary condition at x = 0. An unique solvability theorem of this problem is proved. The inverse problem is devoted to determining the coefficients σ(x) and q(x). As an additional information for recovering this coefficients, two forward problems with different Dirichlet data are considered and traces of the derivative of their solutions with respect to x are given at x = 0 on a finite interval. For the inverse problem a local existence and uniqueness theorem is established.

AB - For the wave equation with inhomogeneity σ(x)umt + q(x)up a forward and an one-dimensional inverse problems are studied. Here m > 1 and p > 1 are real numbers. The forward problem is considered in the domain x > 0, t > 0 with zero initial data and Dirichlet boundary condition at x = 0. An unique solvability theorem of this problem is proved. The inverse problem is devoted to determining the coefficients σ(x) and q(x). As an additional information for recovering this coefficients, two forward problems with different Dirichlet data are considered and traces of the derivative of their solutions with respect to x are given at x = 0 on a finite interval. For the inverse problem a local existence and uniqueness theorem is established.

KW - existence

KW - inverse problem

KW - nonlinear wave equation

KW - uniqueness

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85204995039&origin=inward&txGid=55ca46cd479c220bffbff255ad8bed7a

UR - https://www.webofscience.com/wos/woscc/full-record/WOS:001320677800010

UR - https://www.mendeley.com/catalogue/f2894c22-c282-3794-bc80-bb3f37b474e6/

U2 - 10.32523/2306-6172-2024-12-3-135-162

DO - 10.32523/2306-6172-2024-12-3-135-162

M3 - Article

VL - 12

SP - 135

EP - 162

JO - Eurasian Journal of Mathematical and Computer Applications

JF - Eurasian Journal of Mathematical and Computer Applications

SN - 2306-6172

IS - 3

ER -