On uniqueness of Neumann‐Tricomi problem in R2

Abstract

AbstractWe consider the equation of mixed type equation image (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, dnu: = k(y)uxdy – uydx|γ0 = = Ψ(s) for a “general” function k(y), when r(x, y) is not necessarily zero and Γ1 is of a more general form then in the papers of V. P. Egorov [6], [7].