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Nonlinear partial differential equations and free boundaries

Author: J I Díaz
Publisher: Boston : Pitman Advanced Pub. Program, 1985-
Series: Research notes in mathematics, 106.
Edition/Format:   Print book : EnglishView all editions and formats
Database:WorldCat
Summary:
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  Read more...
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Additional Physical Format: Online version:
Díaz, J.I.
Nonlinear partial differential equations and free boundaries.
Boston : Pitman Advanced Pub. Program, 1985-
(OCoLC)609429312
Document Type: Book
All Authors / Contributors: J I Díaz
ISBN: 0273085727 9780273085720
OCLC Number: 11574715
Notes: Spine title: Nonlinear PDEs and free boundaries.
Description: volumes <1> : illustrations ; 25 cm.
Contents: v. 1. Elliptic equations.
Series Title: Research notes in mathematics, 106.
Other Titles: Nonlinear PDEs and free boundaries
Responsibility: J.I. Diaz.

Abstract:

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.

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