A new class of parabolic problems connected with Newton's polygon

Pages: 294 - 303, Issue Special, September 2007

 Abstract        Full Text (205.9K)              

Robert Denk - Department of Mathematics and Statistics, University of Konstanz, D-78457 Konstanz, Germany (email)
Leonid Volevich - Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, 4 Miusskaya Square, 125047 Moscow, Russian Federation (email)

Abstract: A new class of boundary value problems for parabolic operators is introduced. We discuss some linearized free boundary problems not satisfying the classical parabolicity condition. It is shown that they belong to this class and by means of the Newton polygon method the nontrivial two-sided estimates of these problems are found.

Keywords:  Free boundary value problems, parabolic equations, Lopatinskii matrix, Newton’s polygon.
Mathematics Subject Classification:  35K50, 80A22.

Received: July 2006;      Revised: June 2007;      Published: September 2007.