Boundary dynamics of a two-dimensional diffusive free boundary problem

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April 2010, 26(2): 713-736. doi: 10.3934/dcds.2010.26.713

Boundary dynamics of a two-dimensional diffusive free boundary problem

Micah Webster ^1, and Patrick Guidotti ^2,

1.	Mathematics and Computer Science Department, Goucher College, 1021 Dulaney Valley Road, Baltimore, MD, 21204, United States
2.	Department of Mathematics, University of California, Irvine, CA 92697-3875

Received February 2009 Revised July 2009 Published October 2009

Abstract
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Numerous models of industrial processes such as diffusion in glassy polymers or solidification phenomena, lead to general one-phase free boundary value problems with phase onset. In this paper we develop a framework viable to prove global existence and stability of planar solutions to one such multi-dimensional model whose application is in controlled-release pharmaceuticals. We utilize a boundary integral reformulation to allow for the use of maximal regularity. To this effect, we view the operators as pseudo-differential and exploit knowledge of the relevant symbols. Within this framework, we give a local existence and continuous dependence result necessary to prove planar solutions are locally exponentially stable with respect to two-dimensional perturbations.

Keywords: Free Boundary Problem, Well-Posedness, Non-Regular Pseudodifferential Operators., Maximal Regularity.

Mathematics Subject Classification: Primary: 35A07, 35C15, 35M1.

Citation: Micah Webster, Patrick Guidotti. Boundary dynamics of a two-dimensional diffusive free boundary problem. Discrete & Continuous Dynamical Systems - A, 2010, 26 (2) : 713-736. doi: 10.3934/dcds.2010.26.713

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