Geodesic
The Samarsky--Ionkin problem with integral perturbation for a pseudoparabolic equation
The Bulletin of Irkutsk State University. Series Mathematics, Tome 42 (2022), pp. 59-74

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In the work the solvability of nonlocal boundary value problems for third-order pseudoparabolic equations in anisotropic spaces of Sobolev is studied. The condition is specified by a spatial variable that combines the generalized Samarsky–Ionkin condition and the integral type condition is particularity of the problems under study. The work aim is to prove the existence and uniqueness of the problems regular solutions — the solutions that have all Sobolev derivatives included in the corresponding equation.
Keywords: Sobolev type differential equations of the third order, spatially-nonlocal boundary value problems, generalized Samarsky–Ionkin condition, regular solutions, existence and uniqueness. 
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     author = {A. I. Kozhanov and G. I. Tarasova},
     title = {The {Samarsky--Ionkin} problem with integral perturbation for a pseudoparabolic equation},
     journal = {The Bulletin of Irkutsk State University. Series Mathematics},
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     year = {2022},
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A. I. Kozhanov; G. I. Tarasova. The Samarsky--Ionkin problem with integral perturbation for a pseudoparabolic equation. The Bulletin of Irkutsk State University. Series Mathematics, Tome 42 (2022), pp. 59-74. http://geodesic.mathdoc.fr/item/IIGUM_2022_42_a4/