Email this article Solution of a problem for a system of third order partial differential equations
- Authors: Uskov V.I.1
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Affiliations:
- Voronezh State University of Forestry and Technologies named after G. F. Morozov
- Issue: Vol 26, No 133 (2021)
- Pages: 68-76
- Section: Original articles
- URL: https://bakhtiniada.ru/2686-9667/article/view/296408
- ID: 296408
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Abstract
An initial-boundary value problem for a system of third-order partial differential equations is considered. Equations and systems of equations with the highest mixed third derivative describe heat exchange in the soil complicated by the movement of soil moisture, quasi-stationary processes in a two-component semiconductor plasma, etc. The system is reduced to a differential equation with a degenerate operator at the highest derivative with respect to the distinguished variable in a Banach space. This operator has the property of having 0 as a normal eigenvalue, which makes it possible to split the original equations into an equation in subspaces. The conditions are obtained under which a unique solution to the problem exists; the analytical formula is found.
About the authors
Vladimir I. Uskov
Voronezh State University of Forestry and Technologies named after G. F. Morozov
Author for correspondence.
Email: vum1@yandex.ru
ORCID iD: 0000-0002-3542-9662
Candidate of Physics and Mathematics, Senior Lecturer of the Mathematics Department
Russian Federation, 8 Timiryazeva St., Voronezh 394087, Russian FederationReferences
- A. F. Chudnovskyy, Teplofizika Pochv, Nauka Publ., Moscow, 1976 (In Russian).
- V. L. Ginzburg, A. A. Ruhadze, Volny v Magnitoaktivnoj Plazme, Nauka Publ., Moscow, 1975 (In Russian).
- I. T. Gohberg, M. G. Krein, Vvedenie v Teoriyu Linejnyh Nesamosopryazhennyh Operatorov, Nauka Publ., Moscow, 1965 (In Russian).
- V. F. Chistyakov, A. A.Shcheglova, Izbrannye Glavy Teorii Algebro-Differencial'nyh Sistem, Nauka Publ., Novosibirsk, 2003 (In Russian).
- S.P. Zubova, "On the solvability of the Cauchy problem for a descriptor pseudoregular equation in a Banach space", Bulletin of the Voronezh State University. Series: Physics. Maths, 2013, ќ2, 192-198 (In Russian).
- G. A. Sviridyuk, V. E. Fedorov, "Semigroups of operators with kernels", Bulletin of the Chelyabinsk State University, 2002, № 6, 42-70 (In Russian).
- P. Kunkel, V. Mehrmann, Algebraic Equations: Analysis and Numerical Solution, European Mathematical Society, Germany, 2006.
- A. B. Al'shin, M. O. Korpusov, Yu, D. Pletner, A. G. Sveshnikov, Linejnye i Nelinejnye Uravneniya Sobolevskogo Tipa, Fizmatlit Publ., Moscow, 2007 (In Russian).
- S. M. Wade, I. B. Paul, "A differentiation index for partial differential algebraic equations", SIAM Journal of Scientific Computing, 21:6 (2000), 2295-2316.
- Nguyen Khac Diep, V. F. Chistyakov, "Using Partial Differential Algebraic Equations in Modelling", Vestnik YuUrGU. Ser. Mat. Model. Progr., 6:1 (2013), 98-111 (In Russian).
- S.P. Zubova, E. V. Raetskaya, V. I. Uskov, "On the degeneracy properties of some matrix differential operator and their application", Problems of Mathematical Analysis, 2021, In print (In Russian).
- S. G. Krein, Linejnye Differencial'nye Uravneniya v Banahovom Prostranstve, Nauka Publ., Moscow, 1967 (In Russian).
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