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## Annales Polonici Mathematici

1998 | 70 | 1 | 221-231
Tytuł artykułu

### Application of complex analysis to second order equations of mixed type

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This paper deals with an application of complex analysis to second order equations of mixed type. We mainly discuss the discontinuous Poincaré boundary value problem for a second order linear equation of mixed (elliptic-hyperbolic) type, i.e. the generalized Lavrent'ev-Bitsadze equation with weak conditions, using the methods of complex analysis. We first give a representation of solutions for the above boundary value problem, and then give solvability conditions via the Fredholm theorem for integral equations. In [1], [2], the Dirichlet problem (Tricomi problem) for the mixed equation of second order $u_{xx} + sgn y u_{yy} = 0$ was investigated. In [3], the Tricomi problem for the generalized Lavrent'ev-Bitsadze equation $u_{xx} + sgn y u_{yy} + Au_x + Bu_y + Cu = 0$, i.e. $u_{ξη} + au_ξ + bu_η + cu = 0$ with the conditions: a ≥ 0, $a_ξ + ab - c ≥ 0$, c ≥ 0 was discussed in the hyperbolic domain. In the present paper, we remove the above assumption of [3] and obtain a solvability result for the discontinuous Poincaré problem, which includes the corresponding results in [1]-[3] as special cases.
Słowa kluczowe
EN
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
221-231
Opis fizyczny
Daty
wydano
1998
otrzymano
1997-12-28
poprawiono
1998-08-31
Twórcy
autor
• Department of Mathematics, Peking University, Beijing 100871, China
Bibliografia
• [1] A. V. Bitsadze, Differential Equations of Mixed Type, MacMillan, New York, 1964.
• [2] A. V. Bitsadze, Some Classes of Partial Differential Equations, Gordon and Breach, New York, 1988.
• [3] S. P. Pul'kin, The Tricomi problem for the generalized Lavrent'ev-Bitsadze equation, Dokl. Akad. Nauk SSSR 118 (1958), 38-41 (in Russian).
• [4] G. C. Wen, Conformal Mappings and Boundary Value Problems, Amer. Math. Soc., Providence, R.I., 1992, 137-188.
• [5] G. C. Wen, Oblique derivative problems for linear mixed equations of second order, Sci. in China Ser. A 41 (1998), 346-356.
• [6] G. C. Wen and H. Begehr, Boundary Value Problems for Elliptic Equations and Systems, Longman, Harlow, 1990, 217-272.
Typ dokumentu
Bibliografia
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