WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 15, 2016
The Boundary Value Condition of a Degenerate Parabolic Equation
Author:
Abstract: y Fichera-Oleinik Rule, how to give a homogeneous boundary condition to assure the posedness of the equation ∂xxu + u∂yu − ∂tu = f(x, y, t, u), (x, y, t) ∈ QT = Ω × (0, T), is researched. By introducing a new kind of entropy solution, in which the trace γ(∂u/∂xi), xi = x or y, on the boundary of Ω is avoided. By the parabolic regularization method, the uniformly estimate of the gradient is obtained, and using Kolmogoroff’s theorem, the solvability of the equation in BV (QT ) is obtained.