Geodesic
An inverse problem for pseudoparabolic equation with the mixed boundary condition
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 16 (2023) no. 5, pp. 661-672.

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In this paper we study the inverse problem on identification of the leading coefficient in the pseudoparabolic equation. The problem involves the mixed boundary condition. The unknown coefficient is recovered by additional integral boundary data. The existence and uniqueness of the strong solution are proved. The result concerns with the identification of the hydraulic properties of fissured medium.
Keywords: inverse problem, uniqueness.
Mots-clés : filtration, pseudoparabolic equation, existence 
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Anna Sh. Lyubanova. An inverse problem for pseudoparabolic equation with the mixed boundary condition. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 16 (2023) no. 5, pp. 661-672. http://geodesic.mathdoc.fr/item/JSFU_2023_16_5_a11/

[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 | DOI | Zbl

[2] E.Di Bendetto, M.Pierre, “On the Maximum Principle for Pseudoparabolic Equations”, Indiana University Mathematics Journal, 30 (1981), 821–854 | DOI | MR

[3] H.Gajewski, K.Gröger, K.Zacharias, “Nichtlinear Operatorgleichungen und Operatordifferentialgleichungen”, Mathematische Lehrbücher und Monographien, Abteilung, v. II, Mathematische Monographien, 38, Akademie-Verlag, Berlin, 1974 | MR | Zbl

[4] V.E.Fedorov, N.D.Ivanova, “Inverse problem for Oskolkov's system of equations”, Mathematical Methods in Applied Sciences, 40 (2015), 6123–6126 | DOI | MR

[5] A.I.Kozhanov, “On the solvability of the coefficient inverse problems for equations of Sobolev type (O razreshimosti koeffitsientnikh obratnikh zadach dlya nekotorikh uravnenii sobolevskogo tipa)”, Nauchniye vedomosti Belgorodskogo gosudarstvennogo universiteta. Seriya “Matematika. Phizika”, 5 (2010), 88–98 (in Russian)

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

[7] J.-L.Lions, E.Magenes, Problemes aux Limites Non Homogenes et Applications, v. 1, Travaux et Recherches Mathematiques, 17, Dunod, Paris, 1968 | MR

[8] A.Lorenzi, E.Paparoni, “Identification problems for pseudoparabolic integrodifferential operator equations”, J. Inver. Ill-Posed Probl., 5 (1997), 235–253 | MR | Zbl

[9] A.Sh.Lyubanova, “On the Approximation of a Parabolic Inverse Problem by Pseudoparabolic One”, Journal of Siberian Federal University. Mathematics and Physics, 5 (2012), 326–336

[10] A.Sh.Lyubanova, A.Tani, “On Inverse Problems for Pseudoparabolic and Parabolic Equations of Filtration”, Inverse Probl. Sci. En., 19 (2011), 1023–1042 | DOI | MR | Zbl

[11] 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

[12] A.Sh.Lyubanova, A.Tani, “An inverse problem for pseudoparabolic equation of filtration. The stabilization”, Appl. Anal., 92 (2013), 573–585 | DOI | MR | Zbl

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

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

[15] C.G.Pyatkov, C.N.Shergin, “On Some Inverse Coefficient Problems with the Pointwise Overdetermination for Mathematical Models of Filtration”, Bulletin of the South Ural State University. Ser. Mathematical Modelling, Programming and Computer Software (Bulletin SUSU MMCS), 12 (2019), 82–95 | Zbl

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

[17] W.Rundell, M.Stecher, “The nonpositivity of solutions to pseudoparabolic equations”, Proc. Amer. Math. Soc., 75 (1979), 251–254 | DOI | MR | Zbl

[18] W.Rundell, M.Stecher, “Maximum Principles for Pseudoparabolic Partial Differential Equations”, J. Math. Anal. Appl., 57 (1977), 110–118 | DOI | MR | Zbl

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

[20] T.W.Ting, “Certain Non-Steady Flows of Second-order Fluids”, Arch. Ration Mech. An., 14 (1963), 1–26 | DOI | MR | Zbl