BOUNDARY VALUE PROBLEM IN A DOMAIN WITH DEVIATION FROM THE CHARACTERISTICS FOR ONE NONLINEAR EQUATION OF A MIXED TYPE

Аннотация

Consider the equation
T(U) ≡ K(y)Uxx + N(x)Uyy + C(x, y)U = f(x, y, U), (1)
where K(y), N(x), C(x, y), f(x, y, U) are given functions, when K(t) R 0 and N(t) R 0 for t R 0.
Let Ω be a finite simply connected convex domain on the plane of variables (x, y), bounded for
x > 0, y > 0 by a smooth curve σ with endpoints at the points A(1, 0) and B(0, 1), for x > 0, y < 0 and
with characteristics x < 0, y > 0.