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Tricomi-Protter Problem of nD Mixed Type Equations

J. M. Rassias

Abstract


The Tricomi equation was established, in 1923, by F. G. Tricomi (Atti Accad. Naz. Lincei, 14, 133-247) who was the pioneer of parabolic elliptic and hyperbolic boundary value problems. In 1953, 1954 and 1955 M. H. Protter (J. Rat. Mech. Anal. : 2, 107-114, 1953 ; 3,435-446, 1954; 4, 721-732, 1955) generalized these problems even further for the Tricomi equation in three dimensions. In 1977 the author (Ph.D. Dissertation, Univ. Cal., Berkeley) generalized these results in n dimensions. In 2004, A. Kuzmin ,Frontiers of Fluid Mechanics (World Sci. Publ., Singapore, 285-295) considered the bifurcation of transonic flow over a flattened airfoil. In 2005, G. Wen (Applicable Analysis, 84(12), 1267-1286) investigated the Tricomi problem for second order linear equations of mixed type with parabolic degeneracy. In this paper we investigate the Tricomi- Protter problem of mixed type equations in n dimensions.

Keywords


Tricomi- Protter problem; Mixed type equation; Tricomi equation.

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