prof. dr hab. Piotr Rybka

Ta strona ma swój polski odpowiednik

ul. Banacha 2
02-097 Warszawa, Poland
room: 4290
phone +48 22 55 44 486
fax +48 22 55 44 300
e-mail rybka (at) mimuw . edu . pl

Scientific interests

Differential Equations (singular parabolic equations, Cahn-Hilliard problems, gradient flows, Łojasiewicz inequality), Calculus of Variations (linear growth functionals, BV space), Free Boundary Problems, Singular Curvature Flow, Phase Transitions (crystal growth, Stefan-type problme), Mathematical models of continua and biology.

Current NCN grant HARMONIA

Selected publications (the full list of publications is here)

  1. (with Y. Giga, P.Gorka), Nonlocal spatially inhomogeneous Hamilton-Jacobi equation with unusual free boundary, Discrete Contin. Dyn. Syst., 26 (2010), 493-519.
  2. (with E.Yokoyama, Y. Giga), A microscopic time scale approximation to the behavior of the local slope on the faceted surface under a nonuniformity in supersaturation, Physica D, 237 (2008), 2845-2855.
  3. (with Y. Giga), Facet bending driven by the planar crystalline curvature with a generic nonuniform forcing term, J.Differential Equations 2466, (2009), 2264-2303.
  4. (with P.B.Mucha), A New Look at Equilibria in Stefan-Type Problems in the Plane, SIAM J. Math Anal. 39, (2007), No 4, 1120-1134.
  5. (with M. Luskin), Existence of Energy Minimizers for Magnetostrictive Materials, SIAM J. Math Anal. 36, (2005), 2204-2019
  6. (with Q.Tang, D.Waxman), Evolution in a changing environment: Existence of Solutions, Coll. Math. 98(2003).
  7. (with Y. Giga), Quasi-static evolution of 3-D crystals grown from supersaturated vapor, Adv. Diff. Equations. 15, (2002), 1-15.
  8. On modified crystalline Stefan problem with singular data, J.Differential Eq. 181, (2002), 340-366.
  9. (with K.-H.Hoffmann), Convergence of solutions to Cahn-Hilliard equation, Commun. PDE. , 24 (1999), 1055-1077.
  10. (with K.-H.Hoffmann), Convergence of solutions to equation of quasi-static approximation of viscoelasticity with capillarity, J. Math. Analysis Appl., 226, (1998), 61-81.
  11. The crystalline version of the modified Stefan problem in the plane and its properties, SIAM J.Math. Anal., 30, (1999), No 4., 756-786
  12. Viscous damping prevents propagation of singularities in the system of viscoelasticity, Proc. Royal Soc. Edinburgh A, 127, (1997), 1067-1074.
  13. (with I.Fonseca), Relaxation of multiple integrals in the space BV, Proc. Royal Soc. Edinburgh A, 121, (1992), 321-348.
  14. Dynamical modeling of phase transitions by means of viscoelasticity in many dimensions, Proc. Royal Soc. Edinburgh A, 121, (1992), 101-138.

Here is my cv

Lecture notes:

my own, The BV space in variational and evolution problems, The University of Tokyo, Nov. 1 -- Nov. 10, 2016. The log of changes.

by my guest, MICHAL KOWALCZYK, NONLINEAR THEORY OF LOCALIZED PATTERNS: AN INTRODUCTION, delivered at the Faculty of Mathematics, the University of Warsaw, January 2016

Piotr Rybka