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On uniqueness of Neumann‐Tricomi problem in R 2
Author(s) -
Aziz A. K.,
Schneider M.,
Gilbert R. P.
Publication year - 1980
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.1670020204
Subject(s) - mathematics , uniqueness , bounded function , piecewise , mathematical analysis , zero (linguistics) , function (biology) , type (biology) , combinatorics , line (geometry) , uniqueness theorem for poisson's equation , jordan curve theorem , geometry , ecology , philosophy , linguistics , evolutionary biology , biology
We consider the equation of mixed type( k ( y ) ⪌ 0 whenever y ⪌ 0) in a region G which is bounded by the curves: A piecewise smooth curve Γ lying in the half‐plane y > 0 which intersects the line y = 0 at the points A (‐1, 0) and B (0, 0). For y < 0 by a piecewise smooth curve Γ through A which meets the characteristic of (1) issued from B at the point P and the curve Γ which consists of the portion PB of the characteristic through B . We obtain sufficient conditions for the uniqueness of the solution of the problem L [ u ] = f , d n u : = k ( y ) u x d y – u y d x |γ0 = = Ψ( s ) for a “general” function k ( y ), when r ( x, y ) is not necessarily zero and Γ 1 is of a more general form then in the papers of V. P. Egorov [6], [7].