prof. dr hab. Piotr Rybka

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, Calculus of Variations, Free Boundary Problems, Singular Curvature Flow, Phase Transitions (crystal growth, martensitic phase transitions in solids), Mathematical models of continua and biology.

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