Huashui Zhan, "The Boundary Value Condition of a Degenerate Parabolic Equation," WSEAS Transactions on Mathematics, vol. 15, pp. 63-72, 2016, DOI:
Huashui Zhan. The Boundary Value Condition of a Degenerate Parabolic Equation.
WSEAS Transactions on Mathematics. 2016;15:63-72.
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.
Keywords:
Degenerate parabolic equation, Fichera-Oleinik Rule, boundary value condition, entropy solution, trace.
Pages: 63-72 WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 15, 2016, Art. #7 DOI: *As the DOI is a unique identifier, it is already available in the pdf version.
**The DOI link will be activated in the first midst of January 2026.
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