A 2-D free boundary problem with onset of a phase and by Guidotti P.

By Guidotti P.

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Astarita, G. and Sarti, G. , A class of mathematical models for sorption of swelling solvents in glassy polymers, Polymer Engng. , 18 (1978), 388–395. Cohen, D. S. , Free boundary problems in controlled release pharmaceuticals. I. Diffusion in glassy polymers, SIAM J. Appl. , 48 (1988), 1415–1465. Escher, J. , Maximal regularity for a free boundary problem, NoDEA, 2 (1995), 463–510. Escher, J. , Classical solutions of multidimensional Hele-Shaw models, SIAM J. MAth. , 28 (1997),1028–1047. Escher, J.

The question of global existence remains open. 2. The results concerning singular BVPs of Section 2 can be generalized to higher dimensions if the domain degeneration only occurs in one direction. Indeed the nature of the symbols involved is not affected in this case. Multidirectional degenerations remain an open problem. Acknowledgements The author gratefully acknowledges the support of the Swiss National Science Foundation. , Gurnee, E. F. , Diffussion in glassy polymers, J. Polymer Sci. Part C, 12 (1966), 249–261.

MAth. , 28 (1997),1028–1047. Escher, J. , A, center manifold analysis for the Mullins-Sekerka models, J. Diff. , 143 (1998), 267–292. , Singular quasilinear abstract Cauchy problems, Nonlin. Anal. TMA, 32 (1998), 667–695. Guidotti, P. and Pelesko, J. , Transient Instability in Case II Diffusion, Journal of Polymer Science, Part B: Polymer Physics, 36 (1998), 2941–2947. , Partial Differential Equations, Springer, New York, 1982. , Analytic Semigroups and Optimal Regularity in Parabolic Problems, Birkh¨auser, Basel, 1995.

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