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. In 1953 and 1955, M. H. Protter generalized these problems even further. In 1977, we generalized these results in several n-dimensional simply connected domains. In 1950-1951, M. A. Lavrentjev and A. V. Bitsadze investigated the Bitsadze - Lavrentjev equation. In 1990, we proposed the exterior Tricomi problem. 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 2011, we established the exterior Tricomi and Frankl problems for quaterelliptic - quaterhyperbolic equations. In 2014, D. Amanov and J. M. Rassias investigated boundary value problems for the higher order generalized mixed-parabolic equation. In this paper we investigate the exterior Bitsadze-Lavrentjev problem for quaterelliptic -quaterhyperbolic Bitsadze-Lavrentjev PDEquations with eight parabolic lines in a doubly connected domain and propose open problems. These problems are of vital importance in fluid mechanics.

Tbilisi Mathematical Journal, Vol. 7(2) (2014), pp. 111-136