Free-Boundary Problem for a Singular Diffusion Equation
β Scribed by P.Y.H. Pang; H.Y. Wang; J.X. Yin
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 120 KB
- Volume
- 265
- Category
- Article
- ISSN
- 0022-247X
No coin nor oath required. For personal study only.
β¦ Synopsis
In this paper, we study the free-boundary problem associated with a singular diffusion equation. An entropy equality derived by the authors for BV solutions in an earlier paper is used in its formulation. Existence, uniqueness, and regularity results are obtained.
π SIMILAR VOLUMES
## Abstract For a nonlinear diffusion equation with a singular Neumann boundary condition, we devise a difference scheme which represents faithfully the properties of the original continuous boundary value problem. We use nonβuniform mesh in order to adequately represent the spatial behavior of the
Strong solvability in the Sobolev space W 2 p is proved for the oblique derivative problem almost everywhere in βu/β + Ο x u = Ο x in the trace sense on β in the case when the vector field x has a contact of infinite order with β at the points of some non-empty subset E β β .
## Abstract In this paper, we study discontinuous solutions of a partial differential equation of strongly degenerate parabolic type. A notion of weak solutions of __BV__ class is proposed, and existence and uniqueness results are obtained.