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Some second-order systems of partial differential equations of composite type

Published online by Cambridge University Press:  14 November 2011

Lin Wei
Lin Wei
Affiliation:
Department of Mathematics, Zhongshan University, Guangzhou, People's, Republic of China
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Synopsis

The Cauchy problem and the Dirichlet-Cauchy type problem of some second-order systems of partial differential equations of composite type of two unknown functions are investigated. Such systems possess some of the characteristics not only of elliptic but also of hyperbolic systems in the same domain. Representations of the solutions are found for the upper half plane. To this end, the composite systems are reduced to the canonical form by means of successive applications of three kinds of linear transformations. Function theoretic methods are used to obtain representation formulae. Furthermore, some composite systems of 2m-unknown function are also considered.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 106 , Issue 1-2 , 1987 , pp. 73 - 88
Copyright
Copyright © Royal Society of Edinburgh 1987

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References

1Gilbert, R. P. and Schneider, M.. On a class of boundary value problems for a composite system of first order differential equations. J. Approx. Theory 25 (1979), 105–119.CrossRefGoogle Scholar
2Begehr, H.. Boundary value problem for mixed kind systems of first order partial differential equations. 3rd Romanian-Finnish Seminar on Complex Analysis, Bucharest, 1976.Google Scholar
3Dzuraev, A.. Systems of Equations of Composite Type (Moscow: Nauke, 1972).Google Scholar
4Andryn, A. A.. Boundary value problem for the systems of second-order equations of composite type with constant coefficients. Izv. Akad. Nauk Armyan. SSR Ser. Mat. 15 (1980), 154–160 (in Russian).Google Scholar
5Gabov, S. A. et al. On a composite equation connected with the oscillation of a stationary compressible fluid. Differential Equations (Differencial'nye Uravneniya) 19 (1983), 1171–80.Google Scholar
6Lin, C. C.. On the stability of two-dimensional parallel flows. Part I. General theory. Quart.Appl. Math. 3 (1945), 117–142.CrossRefGoogle Scholar
7Keng, Hua Loo, Wei, Lin and Ci-Quian, Wu. Second-order Systems of Partial Differential Equations in the Plane (London: Pitman, 1985).Google Scholar