Publications of Piotr Rybka

  1. M.H. Giga, Y. Giga, P.Rybka, A comparison principle for singular diffusion equations with spatially inhomogeneous driving force, preprint.
  2. Piotr B. Mucha, Piotr Rybka, A note on a model system with sudden directional diffusion, J. Statistical Physics, DOI:10.1007/s10955-012-0446-5.
  3. Karolina Kielak, Piotr B. Mucha, Piotr Rybka, Almost classical solutions to the total variation flow, preprint.
  4. M. Korzec, P. Rybka, On a higher order convective convective Cahn-Hilliard type equation, preprint.
  5. M. Korzec, P. Nayar, P. Rybka, Global weak solutions to a sixth order Cahn-Hilliard type equation, preprint.
  6. Y. Giga, P.Górka, P.Rybka, A Comparison Principle for Hamilton-Jacobi equations with discontinuous Hamiltonians, Proc. AMS. 139, (2011), 1777-1785. (preprint.)
  7. W. Merz, P.Rybka, Strong Solution to the Richards Equation in the Unsaturated Zone, J. Math. Anal. Appl., 371, (2010), 741-749. URL: DOI:10.1016/j.jmaa.2010.05.066
  8. P.Górka, P.Rybka, Existence and uniqueness of solutions to singular ODE's, Arch. Math., 94, (2010), 227-233.
  9. Y. Giga, P.Górka, P.Rybka, Nonlocal spatially inhomogeneous Hamilton-Jacobi equation with unusual free boundary, Discrete Contin. Dyn. Syst., 26, (2010), 493-519.
  10. E.Yokoyama, Y. Giga, P.Rybka, 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.
  11. G.Raugel, P.Rybka, Convergence of solutions of the system of linear visco-elasticity coupled with the Cahn-Hilliard equation, in preparation.
  12. D.Hilhorst, P.Rybka, Stabilization of solutions to a FitzHugh-Nagumo type system, J. Statistical Physics, 138, (2010), 291-304. The original publication is available at www.springerlink.com:
  13. P. Rybka, M. Luskin, Thin Film Limit for Magnetostrictive Crystals, in preparation.
  14. P.B. Mucha, P.Rybka, A caricature of a singular curvature flow in the plane, Nonlinearity, 21, (2008), 2281-2316.
  15. Y. Giga, P.Rybka, Facet bending driven by the planar crystalline curvature with a generic nonuniform forcing term, J.Differential Equations, 246, (2009), 2264-2303.
  16. P.B. Mucha, P.Rybka, A new look at equilibria in Stefan type problems in the plane SIAM J. Math. Anal. 39, No. 4, (2007), 1120-1134;
    URL: DOI: 10.1137/060677124
  17. Y. Giga, P.Rybka, Facet bending in the driven crystalline curvature flow in the plane, The Journal of Geometric Analysis 18, No 1, (2008), 99-132.
  18. P.Rybka, Convergence of a heat flow on a Hilbert manifold, Proceedings of the Royal Society of Edinburgh, Series A, 136 (2006), no. 4, 851-862.
  19. Y. Giga, P. Rybka, Stability of facets of crystals growing from vapor, Discrete Contin. Dyn. Syst. 14 (2006), no. 4, 689-706.
  20. Y. Giga, P.Rybka, Stability of facets of self-similar motion of a crystal, Advances in Differential Equation, 10, Number 6, (2005), 601-634.
  21. P. Rybka, M. Luskin, Existence of Energy Minimizers for Magnetostrictive Materials, SIAM J. Math. Anal. 36, No. 6, (2005) pp. 2004-2019.
  22. Y. Giga, P.Rybka, Existence of self-similar evolution of crystals grown from supersaturated vapor, Interfaces Free Bound. 6 (2004), 405-421.
  23. Y. Giga, P.Rybka, Berg's effect, Adv. Math. Sci. Appl., 13 no 2 (2003), 625-637.
  24. W. Merz, P.Rybka, A Free Boundary Problem Describing Reaction-Diffusion Problems in Chemical Vapor Infiltration of Pyrolytic Carbon J. Math. Anal. Appl., 292 (2004), 571-588.
  25. P.Rybka, Q.Tang, D.Waxman, Evolution in a changing environment: Existence of Solutions, Coll. Math. 98, no 1 (2003).
  26. Y. Giga, P.Rybka, Quasi-static evolution of 3-D crystals grown from supersaturated vapor, Diff. Integral Equations. 15 no 1 (2002), 1-15.
  27. Y. Giga, M.Paolini, P.Rybka, On the motion by singular interfacial energy, Japan J. Indust. Appl. Math. 18, (2001), 231-248.
  28. P.Rybka, On modified crystalline Stefan problem with singular data, J.Differential Equations, 181, (2002), 340-366.
  29. P.Rybka and K.-H.Hoffmann, Analyticity of the nonlinear term forces convergence of solutions to two equations of continuum mechanics, Nonlinear Analysis: Theory, Methods & Applications, Vol. 50 (3) (2002) pp. 409 -424.
  30. P.Rybka, On convergence of solutions of the crystalline Stefan problem with Gibbs-Thomson law and kinetic undercooling, Interfaces Free Bound., 2 (2000), 361-379.
  31. P.Rybka and K.-H.Hoffmann, On convergence of solutions to the equation of viscoelasticity with capillarity, Commun. PDE., 25 (2000), 1845-1890.
  32. P.Rybka and K.-H.Hoffmann Convergence of solutions to Cahn-Hilliard equation, Commun. PDE. 24 (1999), 1055-1077.
  33. P.Rybka and K.-H.Hoffmann Convergence of solutions to equation of quasi-static approximation of viscoelasticity with capillarity, J. Math. Analysis Appl. 226, (1998), 61-81.
  34. P.Rybka The crystalline version of the modified Stefan problem in the plane and its properties, SIAM J.Math. Anal. 30, (1999), No 4., 756-786
  35. P.Rybka Crystalline version of the Stefan problem with Gibbs-Thompson law and kinetic undercooling, Advances in Differential Equations, 3, (1998), 687-713.
  36. P.Rybka Viscous damping prevents propagation of singularities in the system of viscoelasticity, Proc. Royal Soc. Edinburgh A 127 (1997), 1067-1074.
  37. P.Rybka A crystalline motion: uniqueness and geometric properties, SIAM J. Appl. Math. 57 (1997), 53-72.
  38. P.Rybka A quasi-steady approximation to an integro-differential model of interface motion, Applicable Analysis 56 (1995), 19-34.
  39. P.Rybka A priori estimates for gradient of solution to system of viscoelasticity in many dimensions, Topol. Method in Nonlinear Anal. 3 (1994) 235-256.
  40. I.Fonseca, P.Rybka Relaxation of multiple integrals in the space $BV (\Omega; {\bf R}^p)$, Proc. Royal Soc. Edinburgh A, 121, (1992), 321-348.
  41. P.Rybka Dynamical modeling of phase transitions by means of viscoelasticity in many dimensions, Proc. Royal Soc. Edinburgh A, 121, (1992), 101-138.
  42. P.Rybka, Propagation of weak singularities on characteristic surfaces of non-constant multiplicity, Ann. Polon. Math. 49, (1988), 82-92.
  43. P.Rybka, The behaviour of weak singularities on characteristic surfaces with multiplicity change, Bull. Polish Acad. Sci. Math. 32, (1984), 675-679.

Conference proceedings

  1. Piotr B. Mucha, Piotr Rybka, Almost classical solutions of static Stefan type problems involving crystalline curvature, in: ``Nonlocal and Abstract Parabolic Equations and their Applications", Eds: Piotr Mucha, Marek Niezgódka and Piotr Rybka, Banach Center Publ. 86, IMPAN, Warszawa, 2009, 223-234.
  2. Y.Giga, P.Rybka, Faceted crystals grown from solution - a Stefan type problem with a singular interfacial energy GAKUTO International Series Mathematical Sciences and Applications, Vol. 28 (2008) Proceedings of the 4th JSAM-SIMAI seminar on Industrial and Applied Mathematics, ed. H.Fujita, M.Nakamura, pp. 31-43
  3. Y.Giga, P.Rybka, A Stefan type problem arising in modeling ice crystals growing from vapor, Surikaisekikenkyusho Kokyuroku [RIMS Proceedings], No 1428 (2005), 72-83
  4. P.Rybka, The modified crystalline Stefan problem: evolution of broken facets, Surikaisekikenkyusho Kokyuroku [RIMS Proceedings], No 1210 (2001) 142-155.
  5. P.Rybka, K.-H.Hoffmann, Convergence theorems for equations related to phase transitions Zeitschrift für Angewandte Mathematik und Mechanik, 79 Suppl.2 (1999), S785-S786.
  6. P.Rybka, Crystalline Stefan problem in the plane with Gibbs-Thompson law and kinetic undercooling Zeitschrift für Angewandte Mathematik und Mechanik, 78 Suppl.2 (1998), S697-S698.

Edited volumes


``Nonlocal and Abstract Parabolic Equations and their Applications", Eds: Piotr Mucha, Marek Niezgódka and Piotr Rybka, Banach Center Publ. 86, IMPAN, Warszawa, 2009


Textbooks

"Hyperbolic problems", in: ``A problem book on PDE's" (in Polish), the Faculty of Mathematics, Informatics and Mechanics of the University of Warsaw, 2010, ed. P.Strzelecki. P.Rybka co-ordinator of the project.

Piotr Rybka