Solvability of the linear inverse problem for the pseudoparabolic equation
https://doi.org/10.25587/SVFU.2023.85.20.006
Abstract
We investigate the solvability of inverse problems of determination, along with the solution u(x, t) to the pseudoparabolic equation, of the unknown source function. Similar problems are considered when studying wave processes, filtration in porous media, and heat transfer processes. A theorem for the existence of a regular solution is proved. Inverse problems for pseudoparabolic equations with an unknown external influence depending on x and a final redefinition have not been considered previously.
About the Author
O. Yu. Nikolaev
Buryat State University
Russian Federation
Russian Federation
Oleg Yu. Nikolaev
24a Smolin Street, Ulan-Ude 670000
References
1. Sveshnikov A. G., Alshin A. B., Korpusov M. O., and Pletner U. D., Linear and Nonlinear Equations of Sobolev Type [in Russian], Fizmatlit, Moscow (2007).
2. Rundell W., “Determination of an unknown nonhomogeneous term in a linear partial differential equation from overspecified boundary data,” Appl. Anal., 10, 231–242 (1980).
3. Lyubanova A. Sh., “On the appoximation of a parabolic inverse problem by pseudoparabolic one,” J. Sib. Fed. Univ., Ser. Math. Phys., 5, No. 3, 326–336 (2012).
4. Lyubanova A. Sh. and Tani A., “Inverse problems for the stationary and pseudoparabolic equation of diffusion,” Appl. Anal., 98, 1997–2010 (2019).
5. Lyubanova A. Sh., “Inverse problem for a linear pseudo-parabolic equation of filtration type [in Russian],” Obrazov. Resursy i Tekhnol., 2, No. 14, 357–363 (2016).
6. Mamausupov M. Sh., “On the problem of determining the coefficients of a pseudoparabolic equation [in Russian],” in: Research on Integro-Differential Equations, vol. 16, pp. 290–297, Ilim, Frunse (1983).
7. Kozhanov A. I., “On the solvability of inverse coefficient problems for same Sobolev-type equations [in Russian],” Nauch. Vedom. Belgorod. Univ., 18, No. 52, 88–97 (2010).
8. Sobolev S. L., Some Applications of Functional Analysis in Mathematical Physics [in Russian], Nauka, Moscow (1988).
9. Ladyzhenskaya O. A., Boundary Value Problems of Mathematical Physics [in Russian], Nauka, Moscow (1973).
10. Jakubov S. Ja., Linear Differential Operator Equations and Their Applications [in Russian], Elm, Baku (1985).
Review
For citations:
Nikolaev O.Yu. Solvability of the linear inverse problem for the pseudoparabolic equation. Mathematical notes of NEFU. 2023;30(3):58-66. (In Russ.) https://doi.org/10.25587/SVFU.2023.85.20.006
Views:
10
JATS XML
Email this article 