A dynamical mother body in a Hele-Shaw problem

Gustafsson, 2006 Di Benedetto, 1984, The ill-posed Hele-Shaw model and the Stephan problem for supercooled water, Trans. Amer. Math. Soc., 282, 183, 10.1090/S0002-9947-1984-0728709-6 Hohlov, 1994, A model for non-smooth free-boundaries in Hele-Shaw flows, Quart. J. Mech. Appl. Math., 47, 107, 10.1093/qjmam/47.1.107 Howison, 1986, Cusp development in Hele-Shaw flow with a free surface, SIAM J. Appl. Math., 46, 20, 10.1137/0146003 Polubarinova-Kochina, 1945, On a problem of the motion of the contour of a petroleum shell, Prikl. Matem. Mech., 9, 79 Polubarinova-Kochina, 1945, Concerning unsteady motions in the theory of filtration, Dokl. Akad. Nauk USSR, 47, 254 Galin, 1945, Unsteady filtration with a free surface, Dokl. Acad. Nauk USSR, 47, 246 Siegel, 1996, Singular effects of surface tension in evolving Hele-Shaw flows, J. Fluid Mech., 323, 201, 10.1017/S0022112096000894 Bettelheim, 2006, Tip-splitting evolution in the idealized Saffman–Taylor problem, J. Phys. A, 39, 1759, 10.1088/0305-4470/39/7/018 Lee, 2006, Bubble break-off in Hele-Shaw flows—singularities and integrable structures, Physica D, 219, 22, 10.1016/j.physd.2006.05.010 Davis, 1979 D. Khavinson, Holomorphic partial differential equations and classical potential theory, Universidad de La Laguna, 1996. Shapiro, 1992 Savina, 2010, On the dependence of the reflection operator on boundary conditions for biharmonic functions, J. Math. Anal. Appl., 370, 716, 10.1016/j.jmaa.2010.04.036 T. Savina, On non-local reflection for elliptic equations of the second order in R2 (the Dirichlet condition), Trans. Amer. Math. Soc. (in press). Howison, 1992, Complex variable methods in Hele-Shaw moving boundary problems, European J. Appl. Math., 3, 209, 10.1017/S0956792500000802 Cummings, 1999, Two-dimensional Stokes and Hele-Shaw flows with free surfaces, European J. Appl. Math., 10, 635, 10.1017/S0956792599003964 Khavinson, 2009, Planar elliptic growth, Complex Anal. Oper. Theory, 3, 425, 10.1007/s11785-008-0093-7 B. Gustafsson, Lectures on balayage, in Clifford algebras and potential theory, Univ. Joensuu, Joensuu, 2004, pp. 17–63. Gustafsson, 2005, What is a quadrature domain? Zidarov, 1968, On solution of some inverse problems for potential fields and its application to questions in geophysics, Publ. House Bulgar. Acad. Sci., Sofia Zidarov, 1990 Gustafsson, 1998, On mother bodies of convex polyhedra, SIAM J. Math. Anal., 29, 1106, 10.1137/S0036141097317918 Gustafsson, 1999, On potential theoretic skeletons of polyhedra, Geom. Dedicata, 76, 1, 10.1023/A:1005184009159 Sjödin, 2006, Mother bodies of algebraic domains in the complex plane, Complex Variables and Elliptic Equations, 51, 357, 10.1080/17476930600610049 A.V. Tsirulskii, Functions of complex variable in the theory and methods of potential geophysical fields, URO AN SSSR, Sverdlovsk, 1990 (in Russian). T.V. Savina, B.Yu. Sternin, V.E. Shatalov, Notes on mother body in geophysics, Preprint Max-Planck Institut fur Mathematik, Bonn, MPI/95-90, p. 23. Savina, 2005, On a minimal element for a family of bodies producing the same external gravitational field, Appl. Anal., 84, 649, 10.1080/00036810500078845