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A new approach to quasilinear equations of mixed type in general domains

Progress in Natural Science:Materials International 1999年第8期 21-27页

作者：闻国椿 Beijing 100871 China Department of Mathematics Peking University

The oblique derivative boundary value problem for quasilinear second order equations of mixed (elliptic-hyperbolic) type in general domains is considered. Using a new method, the unique solvability of the above bounda... 详细信息

关键词： oblique derivative problem equations of mixed type general domains.

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The Exterior Tricomi Problem for Generalized mixed equations with Parabolic Degeneracy

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Acta Mathematica Sinica,English Series 2006年第5期22卷 1385-1398页

作者： Guo Chun WEN LMAM School of Mathematical Sciences Peking University Beijing 100871 P. R. China

This paper deals with the exterior Tricomi problem for generalized mixed equations with parabolic degeneracy. Firstly the representation of solutions of the problem for the equations is given, and then the uniqueness ... 详细信息

关键词： Exterior Tricomi problem equations of mixed type Doubly connected domain

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Oblique derivative problem for general Chaplygin-Rassias equations

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Science China Mathematics 2008年第1期51卷 5-36页

作者： WEN GuoChun LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, China LMAM School of Mathematical Sciences Peking University Beijing China

The present paper deals with the oblique derivative problem for general second order equations of mixed (elliptic-hyperbolic) type with the nonsmooth parabolic degenerate line $$K_1 (y)u_{xx} + \left| {K_2 (x)} \right|u_{yy} + a(x,y)u_x + b(x,y)u_y + c(x,y)u = - d(x,y)$$ in any plane domain D with the boundary ?D=Γ ∪ L 1 ∪ L 2 ∪ L 3 ∪ L 4, where Γ(? {y > 0}) ∈ C μ 2 (0 equationsequations\frac{{\partial u}}{{\partial \nu }} = \fracequations{{H(x,y)}}\operatorname{Re} \left[ {\overline {\lambda (z)} u_{\tilde z} } \right] = r(z), z \in \Gamma \cup L_1 \cup L_4 , \operatorname{Im} \left[ {\overline {\lambda (z)} u_{\tilde z} } \right]\left| {_{z = z_l } } \right. = b_l ,l = 1,2, u( - 1) = b_0 ,u(1) = b_3 ,$$ in which z 1, z 2 are the intersection points of L 1, L 2, L 3, L 4 respectively. The above equations can be called the general Chaplygin-Rassias equations, which include the Chaplygin-Rassias equations $$K_1 (y)(M_2 (x)u_x )_x + M_1 (x)(K_2 (y)u_y )_y + r(x,y)u = f(x,y), in D$$ as their special case. The above boundary value problem includes the Tricomi problem of the Chaplygin equation: K(y)u xx+u yy = 0 with the boundary condition u(z) = ?(z) on Γ ∪ L 1 ∪ L 4 as a special case. Firstly some estimates and the existence of solutions of the corresponding boundary value problems for the degenerate elliptic and hyperbolic equations of second order are discussed. Secondly, the solvability of the Tricomi problem, the oblique derivative problem and Frankl problem for the general Chaplygin-Rassias equations are proved. The used method in this paper is different from those in other papers, because the new notations W(z) = W(x + iy) = $u_{\tilde z} $ = [H

关键词： oblique derivative problem equations of mixed type nonsmooth degenerate line 35J70 35L80 35N99

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