Title: Nonlinearpartial differential equations and free boundaries
First published: 1985
Description: In this Research Note the author brings together the body of known work and presents many recent results relating to nonlinear partial differential equations that give rise to a free boundary--usually the boundary of the set where the solution vanishes identically. The formation of such a boundary depends on an adequate balance between two of the terms of the equation that represent the particular characteristics of the phenomenon under consideration: diffusion, absorption, convection, evolution etc. These balances do not occur in the case of a linear equation or an arbitrary nonlinear equation. Their characterization is studied for several classes of nonlinear equations relating to applications such as chemical reactions, non-Newtonian fluids, flow through porous media and biological populations. In this first volume, the free boundary for nonlinear elliptic equations is discussed. A second volume dealing with parabolic and hyperbolic equations is in preparation.
Subjects: Boundary value problems, Differential equations, Nonlinear, Differential equations, Partial, Nonlinear Differential equations, Partial Differential equations