TY - CHAP
T1 - The Application of Spectral Resolution of a Self-Adjoint Operator to Approximate Elliptic Source Identification Problem with Neumann-Type Integral Condition
AU - Ashyralyyev, Charyyar
AU - Cay, Aysel
N1 - Publisher Copyright:
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.
PY - 2024
Y1 - 2024
N2 - The paper focuses on the study of an elliptic source identification problem (SIP) with an integral condition for derivatives. Absolute stable difference scheme (DS) is proposed. Stability inequalities for solution of DS are established. Primarily DS is converted to auxiliary difference problem with some non local condition. Uniqueness and existence solution of DS is achieved by applying spectral resolution of a self-adjoint operator. Later, obtained results are used to establish stability inequalities for solution of DS for Neumann-type elliptic multidimensional SIP with integral condition. Finally, numerical illustration for 2D test example is carried out.
AB - The paper focuses on the study of an elliptic source identification problem (SIP) with an integral condition for derivatives. Absolute stable difference scheme (DS) is proposed. Stability inequalities for solution of DS are established. Primarily DS is converted to auxiliary difference problem with some non local condition. Uniqueness and existence solution of DS is achieved by applying spectral resolution of a self-adjoint operator. Later, obtained results are used to establish stability inequalities for solution of DS for Neumann-type elliptic multidimensional SIP with integral condition. Finally, numerical illustration for 2D test example is carried out.
UR - http://www.scopus.com/inward/record.url?scp=85202545148&partnerID=8YFLogxK
U2 - 10.1007/978-3-031-62668-5_10
DO - 10.1007/978-3-031-62668-5_10
M3 - Chapter
AN - SCOPUS:85202545148
T3 - Trends in Mathematics
SP - 101
EP - 114
BT - Trends in Mathematics
PB - Springer Science and Business Media Deutschland GmbH
ER -