By Guidotti P.
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Extra resources for A 2-D free boundary problem with onset of a phase and singular elliptic boundary value problems
Operator-Valued Fourier Multipliers, Vector-Valued Besov-Spaces and Applications, Math. , 186 (1997), 5–56. , Linear and Quesilinear Parabolic Problems, vol II, Birkh¨auser, Basel, in preparation. 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.
Equ. 1. It is natural to ask the question about maximal or global existence for the solution. A distinction need to be made between the two cases δ = 0 and δ > 0. 7) generically cross in ﬁnite time. It is not clear if any beneﬁt could come from the coupling to singular BVPs. In the second case it is possible to continue the solution to its maximal existence interval with the same technique used in the above existence proof. 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.
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. , Operator-Valued Fourier Multipliers, Vector-Valued Besov-Spaces and Applications, Math.