WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 16, 2017
How to Determine the Boundary Condition of a Strongly Degenerate Parabolic Equation
Author:
Abstract: By reviewing Fichera-Oleˇinik theory, the portion of the boundary on which we should give the boundary value is determined, the corresponding initial-boundary value problem of the strongly degenerate parabolic equation (∂u/∂t)= ΔA(u) + div(b(u, x, t)), (x, t) ∈ Ω × (0, T), is considered. By introducing a new kind of entropy solution, we are able to get the existence and the stability of the solutions.