BOUNDARY DYNAMICS OF A TWO-DIMENSIONAL DIFFUSIVE FREE BOUNDARY PROBLEM
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Type of Work24 pages
ProgramCenter for Data, Mathematical, and Computational Sciences
Citation of Original PublicationM. Webster, P. Guidotti, “Boundary dynamics of a two-dimensional diffusive free boundary problem,” Discrete and Continuous Dynamical Systems-Series A, Vol. 26 (2) 2010, 713-736.
SubjectsFree Boundary Problem
Non- Regular Pseudodifferential Operators
Numerous models of industrial processes such as diffusion in glassypolymers 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 ex-ploit 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.