Browsing by Subject "Non- Regular Pseudodifferential Operators"
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Item BOUNDARY DYNAMICS OF A TWO-DIMENSIONAL DIFFUSIVE FREE BOUNDARY PROBLEM(2010-02) Webster, Micah; Guidotti, Patrick; Mathematics; Center for Data, Mathematical, and Computational SciencesNumerous 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.