ON Hele-Shaw models with surface tension

Mathematical Research Letters

Volumn 3, Issue 4, 1996, Pages 467-474

  Escher, Joachim ^a   Simonett, Gieri ^b  

^a UNIVERSITY OF BASEL   (Switzerland)

^b VANDERBILT UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030305156     PISSN: 10732780     EISSN: None     Source Type: Journal    
DOI: 10.4310/MRL.1996.v3.n4.a5     Document Type: Article

References (16)

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3. 3. S. B. Angenent, Nonlinear analytic semiflows, Proc. Roy. Soc. Edinburgh 115A (1990), 91-107.
4. 4. X. Chen, The Hele-Shaw problem and area-preserving curve shortening motion, Arch. Rational Mech. Anal. 123 (1993), 117-151.
5. 5. X. Chen, J. Hong, and F. Yi, Existence, uniqueness, and regularity of classical solutions of the Mullins-Sekerka problem, Preprint (1996).
6. 6. P. Constantin and M. Pugh, Global solutions for small data to the Hele-Shaw problem, Nonlinearity 6 (1993), 393-415.
7. 7. C. M. Elliott and J. R. Ockendon, Weak and Variational Methods for Moving Boundary Problems, Pitman, Boston, 1982.
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9. 9. -, Analyticity of the interface in a free boundary problem, Math. Ann., to appear.
10. 10. -, Classical solutions of multi-dimensional Hele-Shaw models, SIAM J. Math. Anal., to appear.
11. 11. -, Classical solutions for Hele-Shaw models with surface tension, Preprint (1996).
12. 12. M. E. Gurtin, Thermomechanics of Evolving Phase Boundaries in the plane, Clarendon Press, Oxford, 1993.
13. 13. S. D. Howinson, Complex variable methods in Hele-Shaw moving boundary problems, European J. Appl. Math. 3 (1992), 209-224.
14. 14. A. A. Lacely, S. D. Howinson, and J. R. Ockendon, Irregular morphologies in unstable Hele-Shaw free boundary problems, Quart. J. Mech. Appl. Math. 43 (1990), 387-405.
15. 15. G. Simonett, Quasilinear parabolic equations and semiflows. In Evolution Equations, Control Theory, and Biomathematics, Lecture Notes in Pure and Appl. Math., M. Dekker, New York, 155, (1994) 523-536.
16. 16. H. Triebel, Theory of Function Spaces, Birkhäuser, Basel, 1983.