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A Space-Dependent Source Identification Problem for Hyperbolic-Parabolic Equations
Department of Software Engineering, Bahcesehir University, Istanbul, 34353, Turkey. (MAM)ORCID iD: 0000-0001-6708-3160
Department of Mathematics, Near East University, Mersin 10, Nicosia, TRNC, Turkey.
Voronezh State University, Universitetskaya 1, Voronezh, 394018, Russian Federation.
2021 (English)In: Springer Proceedings in Mathematics and Statistics, Volume 351, 2021, Vol. 351, p. 183-198Conference paper, Published paper (Refereed)
Abstract [en]

In the present paper, a space-dependent source identification problem for the hyperbolic-parabolic equation with unknown parameter p $$ \left\{ \begin{array}{l} \displaystyle u''(t) + Au(t) = p + f(t), ~ 0<t<1, \\ \displaystyle u'(t) + Au(t) = p + g(t), ~ -1<t<0, \\ \displaystyle u(0^{+})=u(0^{-}), ~ u'(0^{+})=u'(0^{-}), \\ \displaystyle u(-1)=\varphi, ~ \int \limits _{0}^{1} u(z)dz=\psi \end{array} \right. $${u′′(t)+Au(t)=p+f(t),0<t<1,u′(t)+Au(t)=p+g(t),-1<t<0,u(0+)=u(0-),u′(0+)=u′(0-),u(-1)=φ,∫01u(z)dz=ψ in a Hilbert space H with self-adjoint positive definite operator A is investigated. The stability estimates for the solution of this identification problem are established. In applications, the stability estimates for the solutions of four space-dependent source identification hyperbolic-parabolic problems are obtained.

Place, publisher, year, edition, pages
2021. Vol. 351, p. 183-198
National Category
Mathematical Analysis Computational Mathematics
Research subject
Mathematics/Applied Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-56225DOI: 10.1007/978-3-030-69292-6_14Scopus ID: 2-s2.0-85112190160OAI: oai:DiVA.org:mdh-56225DiVA, id: diva2:1603346
Conference
4th International Conference on Analysis and Applied Mathematics ICAAM 2018, Mersin, Turkey, September 6-9, 2018
Available from: 2021-10-15 Created: 2021-10-15 Last updated: 2021-10-28Bibliographically approved

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Ashyraliyev, Maksat

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