Geodesic
The regularity of the solutions of inverse problems for the pseudoparabolic equation
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 14 (2021) no. 4, pp. 414-424.

Voir la notice de l'article provenant de la source Math-Net.Ru

The paper discusses the regularity of the solutions to the inverse problems on finding unknown coefficients dependent on $t$ in the pseudoparabolic equation of the third order with an additional information on the boundary. By the regularity is meant the continuous dependence of the solution on the input data of the inverse problem. The regularity of the solution is proved for two inverse problems of recovering the unknown coefficient in the second order term and the leader term of the linear pseudoparabolic equation.
Keywords: continuous dependence on the input data, a priori estimate, inverse problem
Mots-clés : pseudoparabolic equation. 
@article{JSFU_2021_14_4_a2,
     author = {Anna Sh. Lyubanova},
     title = {The regularity of the solutions of inverse problems for the pseudoparabolic equation},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {414--424},
     publisher = {mathdoc},
     volume = {14},
     number = {4},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2021_14_4_a2/}
}
TY  - JOUR
AU  - Anna Sh. Lyubanova
TI  - The regularity of the solutions of inverse problems for the pseudoparabolic equation
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2021
SP  - 414
EP  - 424
VL  - 14
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JSFU_2021_14_4_a2/
LA  - en
ID  - JSFU_2021_14_4_a2
ER  - 
%0 Journal Article
%A Anna Sh. Lyubanova
%T The regularity of the solutions of inverse problems for the pseudoparabolic equation
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2021
%P 414-424
%V 14
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JSFU_2021_14_4_a2/
%G en
%F JSFU_2021_14_4_a2
Anna Sh. Lyubanova. The regularity of the solutions of inverse problems for the pseudoparabolic equation. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 14 (2021) no. 4, pp. 414-424. http://geodesic.mathdoc.fr/item/JSFU_2021_14_4_a2/

[1] G.I. Barenblatt, Iu.P. Zheltov, I.N. Kochina, “Basic concepts in the theory of seepage of homogeneous liquids in fissured blocks [strata]”, J. Appl. Math. Mech., 24 (1960), 1286–1303 (in Russian) | DOI | Zbl

[2] A.I. Kozhanov, “On the solvability of the coefficient inverse problems for equations of Sobolev type)”, Nauchniye vedomosti Belgorodskogo gosudarstvennogo universiteta. Seriya “Matematika. Phizika”, 2010, no. 5, 88–98 (in Russian)

[3] T.-T. Li, L.W. White, “Total Flux (Nonlocal) Boundary Value Problems for Pseudoparabolic Equation”, Appl. Anal., 16 (1983), 17–31 | DOI | MR | Zbl

[4] Nauka, M., 1967 | MR

[5] A. Sh.Lyubanova, “Inverse Problem for a Pseudoparabolic Equation with Integral Overdetermination Conditions”, Differential Equations, 50 (2014), 502–512 | DOI | MR | Zbl

[6] A. Sh.Lyubanova, A. Tani, “An inverse problem for pseudoparabolic equation of filtration. The existence, uniqueness and regularity”, Appl. Anal., 90 (2011), 1557–1571 | DOI | MR | Zbl

[7] A. Sh.Lyubanova, A.V. Velisevich, “Inverse problems for the stationary and pseudoparabolic equations of diffusion”, Appl. Anal., 98 (2019), 1997–2010 | DOI | MR | Zbl

[8] M. Sh.Mamayusupov, “The problem of determining coefficients of a pseudoparabolic equation”, Studies in integro-differential equations, 16, Ilim, Frunze, 1983, 290–297 (in Russian) | MR

[9] A.I. Prilepko, D.G. Orlovsky, I.A. Vasin, Methods for solving inverse problems in mathematical physics, Marcel Dekker, New York, 2000 | MR | Zbl

[10] S.G. Pyatkov, S.N. Shergin, “On some mathematical models of filtration type”, Bulletin of the South Ural State University. Ser. Mathematical Modelling, Programming and Computer Software (Bulletin SUSU MMCS), 2015, no. 8, 105–116 | Zbl

[11] W. Rundell, “Determination of an unknown nonhomogeneous term in a linear partial differential equation from overspecified boundary data”, Appl. Anal., 10 (1980), 231–242 | DOI | MR | Zbl

[12] R.E. Showalter, T.W. Ting, “Pseudoparabolic partial differential equations”, SIAM J. Math. Anal., 1 (1970), 1–26 | DOI | MR | Zbl

[13] A.G Sveshnikov, A.B. Alshin, M.O. Korpusov, Yu.D. Pletner, Linear and nonlinear equations of the Sobolev type, Physmatlit, M., 2007 (in Russian)