BOUNDARY DYNAMICS OF A TWO-DIMENSIONAL DIFFUSIVE FREE BOUNDARY PROBLEM
| Autor: | Patrick Guidotti, Micah Webster |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2010 |
| Předmět: |
Non- Regular Pseudodifferential Operators
Applied Mathematics Mathematical analysis Phase (waves) Boundary (topology) Maximal Regularity Stability (probability) Free Boundary Problem Well-Posedness Planar Exponential stability Free boundary problem Discrete Mathematics and Combinatorics Boundary value problem Diffusion (business) Analysis Mathematics |
| DOI: | 10.13016/m2cc0tt2h |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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