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

- (with Y. Giga, P.Gorka), Nonlocal spatially inhomogeneous Hamilton-Jacobi
equation with unusual free boundary,
* Discrete Contin. Dyn. Syst.,
***26** (2010), 493-519.
- (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.
- (with Y. Giga), Facet bending driven by the planar crystalline
curvature with a generic nonuniform forcing term,
* J.Differential Equations*** 2466**, (2009), 2264-2303.
- (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.
- (with M. Luskin), Existence of Energy Minimizers for
Magnetostrictive Materials,
* SIAM J. Math Anal. ***
36, **(2005), 2204-2019
- (with Q.Tang, D.Waxman), Evolution in a changing environment:
Existence of Solutions,
* Coll. Math. *** 98**(2003).
- (with Y. Giga), Quasi-static evolution of 3-D crystals grown from supersaturated vapor,
* Adv. Diff. Equations. *** 15,**
(2002), 1-15.
- On modified crystalline Stefan problem with
singular data,
* J.Differential Eq. * ** 181,** (2002), 340-366.
- (with K.-H.Hoffmann), Convergence of solutions to Cahn-Hilliard
equation,
* Commun. PDE. *, ** 24** (1999), 1055-1077.
- (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.
- The crystalline version of the modified Stefan problem
in the plane and its properties,
*
SIAM J.Math. Anal.*, ** 30,** (1999),
No 4., 756-786
- Viscous damping prevents propagation of singularities in
the
system of viscoelasticity,
* Proc. Royal Soc. Edinburgh A*, ** 127,** (1997), 1067-1074.
- (with I.Fonseca), Relaxation of multiple integrals in the
space BV,
* Proc. Royal Soc. Edinburgh A, * ** 121**,
(1992), 321-348.
- 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

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