Electronic Journal of Differential Equations,
Vol. 2009(2009), No. 65, pp. 1-16.
Title: Oblique derivative problems for generalized Rassias equations
of mixed type with several characteristic boundaries
Author: Guo Chun Wen (Peking Univ., Beijing, China)
Abstract:
This article concerns the oblique derivative problems for
second-order quasilinear degenerate equations of mixed type with
several characteristic boundaries, which include the Tricomi problem
as a special case. First we formulate the problem
and obtain estimates of its solutions, then we show the existence
of solutions by the successive iterations and the Leray-Schauder theorem.
We use a complex analytic method: elliptic complex functions
are used in the elliptic domain, and hyperbolic complex functions
in the hyperbolic domain, such that second-order equations of mixed
type with degenerate curve are reduced to the first order mixed complex
equations with singular coefficients.
An application of the complex analytic method, solves
(1.1) below with $m=n=1$, $a=b=0$, which was posed as
an open problem by Rassias.
Submitted December 16, 2008. Published May 14, 2009.
Math Subject Classifications: 35M05, 35J70, 35L80.
Key Words: Oblique derivative problems; generalized Rassias equations;
several characteristic boundaries.