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Existence for a characteristic boundary value problem for an equation of mixed type in three‐dimensional space
Author(s) -
MüllerRettkowski A. H.,
Gilbert P.P.
Publication year - 1983
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670050123
Subject(s) - mathematics , mathematical analysis , space (punctuation) , bounded function , type (biology) , sign (mathematics) , boundary (topology) , image (mathematics) , piecewise , surface (topology) , plane (geometry) , energy (signal processing) , geometry , pure mathematics , ecology , philosophy , linguistics , biology , statistics , artificial intelligence , computer science
The equation of mixed typeWith k ( x 3 ) = sign x 3 | x 3 | m , m > 0, d ϵ C 1 (Ḡ), x = ( x 1 , x 2 , x 3 ), is considered in the threedimensional region G which is bounded by the surfaces: a piecewise smooth surface Γ 0 lying in the half‐space x 3 > 0 which intersects the plane x 3 = 0 in the unit circle, and for x 3 < 0 by the characteristic surfacesWe prove existence of a generalized solution for the characteristic boundary value problem: Lu = f in G , u Γ0∪Γ1 = 0. The result is obtained by using a variant of the energy‐integral method.