Boundary value problems for a model system of first-order equations in three-dimensional space. (English. Russian original) Zbl 1331.35255
Differ. Equ. 51, No. 5, 645-651 (2015); translation from Differ. Uravn. 51, No. 5, 635-641 (2015).
The authors consider the three-dimensional analog of the generalized Cauchy-Riemann system \(\sum_{k=1}^3 E_k U_{x_k} + A(x) U = F(x)\) where \(E_k\) are constant \(4 \times 4\) matrices of the special type, \(A\) and \(F\) are given matrix and vector, respectively. The authors investigate some Riemann-Hilbert problems, in particular, prove their unique solvability.
Reviewer: Vladimir Mityushev (Kraków)
MSC:
| 35Q15 | Riemann-Hilbert problems in context of PDEs |
| 35J56 | Boundary value problems for first-order elliptic systems |
References:
| [1] | Oshorov, Bator B. and Oshorov, Bato B., Elements of the Theory of Functions of Quaternion Variables,in Matematika i metody ee prepodavaniya: Sb. statei (Mathematics and Its Education Methods.Collection of Works), Ulan-Ude, no. 2, 2001, pp. 54-57. · Zbl 1274.30160 |
| [2] | Oshorov, B. B., Elliptic Systems of Equations in Four-Dimensional Space, 31-41 (2002) |
| [3] | Korn, G. and Korn, T., Spravochnik po matematike dlya nauchnykh rabotnikov i inzhenerov (ReferenceBook on Mathematics for Scientists and Engineers), Moscow, 1984. · Zbl 0535.00032 |
| [4] | Berezin, A.V., Kurochkin, Yu.A., and Tolkachev, E.A., Kvaterniony v relyativistskoi fizike (Quaternionsin Relativistic Physics), Moscow, 2003. |
| [5] | Fueter, R., Functions of a Hyper Complex Variable, Zurich, 1948-1949. |
| [6] | Imaeda, K., A New Formulation of Classical Electrodynamics, Nuovo Cimento Soc. Ital. Fis. B, 1976,vol. 32B, no. 1, pp. 138-162. · doi:10.1007/BF02726749 |
| [7] | Lax, P.D. and Philips, R.S., Local Boundary Conditions for Dissipative Symmetric Linear DifferentialOperators, Comm. Pure Appl. Math., 1960, vol. 13, pp. 427-455. · Zbl 0094.07502 · doi:10.1002/cpa.3160130307 |
| [8] | Vragov, V.N., Kraevye zadachi dlya neklassicheskikh uravnenii matematicheskoi fiziki: Uchebnoe posobie(Boundary Value Problems for Nonclassical Equations of Mathematical Physics. Teaching Book),Novosibirsk, 1983. · Zbl 0547.00024 |
| [9] | Oshorov, B.B., On Some Boundary Value Problems for Systems of Cauchy-Riemann and BitsadzeEquations, Dokl. Akad. Nauk, 2006, vol. 407, no. 4, pp. 446-449. |
| [10] | Oshorov, B.B., The Riemann-Hilbert and Poincar´e Problems with Discontinuous Boundary Conditionsfor Some Model Systems of Partial Differential Equations, Differ. Uravn., 2011, vol. 47, no. 5,pp. 696-704. · Zbl 1228.35167 · doi:10.1134/S0012266111050089 |
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