Constructing multiply connected quadrature domains

SIAM Journal on Applied Mathematics

Volumn 64, Issue 4, 2004, Pages 1334-1359

  Crowdy, Darren ^a   Marshall, Jonathan ^a  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

Conformal mapping; Multiply connected; Quadrature domains

Indexed keywords

BOUNDARY CONDITIONS; FUNCTIONS; INTEGRATION; MATHEMATICAL OPERATORS; PROBLEM SOLVING; SET THEORY; THEOREM PROVING;

MEAN VALUE THEOREM; MULTIPLY CONNECTED; QUADRATURE DOMAINS; QUADRATURE IDENTITY;

CONFORMAL MAPPING;

EID: 4544248036     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036139903438545     Document Type: Article

References (25)

1. P. DAVIS, The Schwarz Function and Its Applications, Carus Math. Monogr. 17, Math. Assoc. America, Washington, DC, 1974.
2. D. AHARONOV AND H. SHAPIRO, Domains on which analytic functions satisfy quadrature identities, J. Anal. Math., 30 (1976), pp. 39-73.
3. M. SAKAI, Quadrature Domains, Lecture Notes in Math. 934, Springer-Verlag, New York, 1982.
4. H. S. SHAPIRO, Unbounded quadrature domains, in Complex Analysis I (University of Maryland 1985-86), C. A. Bernstein, ed., Lecture Notes in Math. 1275, Springer-Verlag, Berlin, 1987, pp. 287-331.
5. B. GUSTAFSSON, Quadrature identities and the Schottky double, Acta. Appl. Math., 1 (1983), pp. 209-240.
6. B. GUSTAFSSON, Singular and special points on quadrature domains from an algebra-geometric point of view, J. Anal. Math., 51 (1988), pp. 91-117.
7. S. RICHARDSON, Hele-Shaw flows with a free boundary produced by the injection of fluid into a narrow channel, J. Fluid Mech., 56 (1972), pp. 609-618.
8. V. M. ENTOV, P. I. ETINGOF, AND D. YA KLEINBOCK, On nonlinear interface dynamics in Hele-Shaw flows, European J. Appl. Math., 6 (1995), pp. 399-420.
9. D. G. CROWDY, Theory of exact solutions for the evolution of a fluid annulus in a rotating Hele-Shaw cell, Quart. Appl. Math., 60 (2002), pp. 11-36.
10. D. G. CROWDY AND H. KANG, Squeeze flow of multiply connected fluid domains in a Hele-Shaw cell, J. Nonlinear Sci., 11 (2001), pp. 279-304.
11. D. G. CROWDY, A note on viscous sintering and quadrature identities, European J. Appl. Math., 10 (1999), pp. 623-634.
12. D. G. CROWDY, A class of exact multipolar vortices, Phys. Fluids, 11 (1999), pp. 2556-2564.
13. D. G. CROWDY, Multipolar vortices and algebraic curves, R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci., 457 (2001), pp. 2337-2359.
14. D. G. CROWDY, Circulation-induced deformations of drops and bubbles: Exact two-dimensional models, Phys. Fluids, 11 (1999), pp. 2836-2845.
15. G. VALIRON, Cours d'Analyse Mathematique: Theorie des Fonctions, Masson, Paris, 1947.
16. S. RICHARDSON, Hele-Shaw flows with time-dependent free boundaries in which the fluid occupies a multiply connected region, European J. Appl. Math., 5 (1994), pp. 97-122.
17. L. CARRILLO, J. SORIANO, AND J. ORTIN, Radial displacement of a fluid annulus in a rotating Hele-Shaw cell, Phys. Fluids, 11 (1999), pp. 778-785.
18. D. G. CROWDY AND S. TANVEER, A theory of exact solutions for annular viscous blobs, J. Nonlinear Sci., 8 (1998), pp. 375-400; Erratum, J. Nonlinear Sci., 11 (2001), p. 237.
19. S. RICHARDSON, Plane Stokes flow with time-dependent free boundaries in which the fluid occupies a doubly connected region, European J. Appl. Math., 11 (2000), pp. 249-269.
20. D. G. CROWDY, Viscous sintering of unimodal and bimodal cylindrical packings with shrinking pores, European J. Appl. Math., 14 (2003), pp. 421-445.
21. H. F. BAKER, Abelian Functions: Abel's Theorem and the Allied Theory of Theta Functions, Cambridge University Press, Cambridge, UK, 1995.
22. A. F. BEARDON, A Primer on Riemann Surfaces, London Math. Soc. Lecture Note Ser. 78, Cambridge University Press, Cambridge, UK, 1984.
23. S. RICHARDSON, Hele-Shaw flows with time-dependent free boundaries involving a multiply connected fluid region, European J. Appl. Math., 12 (2001), pp. 571-599.
24. D. MUMFORD, C. SERIES, AND D. WRIGHT, Indra's Pearls: The Vision of Felix Klein, Cambridge University Press, Cambridge, UK, 2002.
25. D. MUMFORD, Tata Lectures on Theta, Birkhäuser Boston, Boston, MA, 1983.