- Tytuł:
- Application of complex analysis to second order equations of mixed type
- Autorzy:
- Wen, Guo
- Powiązania:
- https://bibliotekanauki.pl/articles/1294229.pdf
- Data publikacji:
- 1998
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
discontinuous Poincaré problem
equations of mixed type
complex analytic method - Opis:
- 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.
- Źródło:
-
Annales Polonici Mathematici; 1998, 70, 1; 221-231
0066-2216 - Pojawia się w:
- Annales Polonici Mathematici
- Dostawca treści:
- Biblioteka Nauki
Artykuł