The Exterior Tricomi and Frankl Problems for Quaterelliptic-Quaterhyperbolic Equations with Eight Parabolic Lines (European Journal of Pure and Applied Mathematics, 2011)
The famous Tricomi equation was established in 1923 by F. G. Tricomi who is the pioneer of parabolic elliptic and hyperbolic boundary value problems and related problems of variable type. In 1945 F. I. Frankl established a generalization of these problems for the well-known Chaplygin equation subject to a certain Frankl condition. In 1953 and 1955 M. H. Protter generalized these problems even further by improving the Frankl condition. In 1977 we generalized these results in several ndimensional simply connected domains. In 1990 we proposed the exterior Tricomi problem in a doubly connected domain. In 2002 we considered uniqueness of quasi-regular solutions for a bi-parabolic elliptic bi-hyperbolic Tricomi problem. In 2006 G. C. Wen investigated the exterior Tricomi problem for general mixed type equations. In this paper we establish uniqueness of quasi-regular solutions for the exterior Tricomi and Frankl problems for quaterelliptic - quaterhyperbolic mixed type partial differential equations of second order with eight parabolic degenerate lines and propose certain open problems. These mixed type boundary value problems are very important in fluid mechanics.