Publications of Piotr Rybka

  1. Piotr Rybka, On the Dirichlet problem for the one-dimensional ROF functional, preprint.
  2. Samer Dweik, Piotr Rybka, Ahmad Sabra, The non-convex planar Least Gradient Problem, preprint.
  3. Piotr Rybka, Glen Wheeler, Complete classification of solitons for the surface diffusion flow of entire graphs, preprint.
  4. Danielle Hilhorst, Sabrina Roscani, Piotr Rybka, Convergence of solutions of a one-phase Stefan problem with Neumann   boundary data to a self-similar profile, Nonlinear Differ. Equ. Appl. 31 56, (2024)
  5. Yoshikazu Giga, Michał Łasica, Piotr Rybka, The heat equation with the dynamic boundary condition as a singular limit of problems degenerating at the boundary, Asymptotic Analysis, 135 (2023), 463-508, preprint.
  6. Piotr Rybka, Glen Wheeler, Convergence of solutions to a convective Cahn-Hilliard type equation of the sixth order in case of small deposition rates SIAM Journal on Mathematical Analysis, 55 vol. 5, (2023), 4193-5861 preprint
  7. Tokinaga Namba, Piotr Rybka, Shoichi Sato, Special solutions to the space fractional diffusion problem, (version of record) , Fractional Calculus and Applied Analysis, 25 (2022), 2139-2465
  8. Tomasz Lewiński, Piotr Rybka, Anna Zatorska-Goldstein, The Free Material Design problem for stationary heat equation on low dimensional structures , Nonlinearity 36 (2023), 4501-4521 preprint.
  9. Piotr Rybka, Ahmad Sabra, The planar Least Gradient problem in convex domains: the discontinuous case, Nonlinear Differ. Equ. Appl. (2021) 28, 15, preprint.
  10. Michał Łasica, Piotr Rybka, Existence of \(W^{1,1}\) solutions to a class of variational problems with linear growth on convex domains, Indiana University Math. Journal, 70, (2021), 2427-2450; preprint
  11. Tokinaga Namba, Piotr Rybka, On viscosity solutions of space-fractional diffusion equations of Caputo type , SIAM Journal on Mathematical Analysis 52, (2020), no 1, 653-681. preprint
  12. Tokinaga Namba, Piotr Rybka, Vaughan Voller, Some comments on using fractional derivative operators in modeling non-local diffusion processes, J. Comput. Appl. Math. 381 (2021), 113040, preprint
  13. Yoshikazu Giga, Ryota Nakayashiki, Piotr Rybka, Ken Shirakawa, On boundary detachment phenomena for the total variation flow with dynamic boundary conditions, Journal of Differential Equations, 269, (2020), no 12, 10587-10629. preprint.
  14. Piotr Rybka, Anna Zatorska-Goldstein, A stationary heat conduction problem, Calc. Var. Partial Differential Equations 59 (2020), no. 1, Paper No. 40. preprint.
  15. Michał Kowalczyk, Angela Pistoia, Piotr Rybka, Giusi Vaira, Free boundary problems arising in the theory of maximal solutions of equations with exponential nonlinearities, S?inaire Laurent Schwartz -- EDP et applications (2017-2018), Exp. No. 10, 12 p., doi: 10.5802/slsedp.122 preprint.
  16. Piotr Rybka, Ahmad Sabra, The planar Least Gradient problem in convex domains, the case of continuous datum, Nonlinear Analysis,214 (2022), 112595, preprint.
  17. Yoshikazu Giga, Monika Muszkieta, Piotr Rybka, A duality based approach to the minimizing total variation flow in the space \(H^{-s}\) , Jpn. J. Ind. Appl. Math. 36 (2019), no. 1, 261-286, https://doi.org/10.1007/s13160-018-00340-4.
  18. Atsushi Nakayasu, Piotr Rybka, Integrability of the derivative of solutions to a singular one-dimensional parabolic problem, Topological Methods of Nonlinear Analysis, 52 (2018), 239-257, preprint
  19. Adam Kubica, Piotr Rybka, Katarzyna Ryszewska, Weak solutions of fractional differential equations in a non cylindrical domain, Nonlinear Analysis Series B: Real World Applications, 36 (2017), 154-182, preprint
  20. Wojciech Górny, Piotr Rybka, Ahmad Sabra, Special cases of the planar least gradient problem, Nonlinear Analysis 151 (2017), 66-95, http://dx.doi.org/10.1016/j.na.2016.11.020, preprint
  21. Adam Kubica, Piotr Rybka, Fine singularity analysis of solutions to the Laplace equation: Berg's effect, Math. Meth. Appl. Sci., 39, (2016), 1069-1075, preprint
  22. Y. Giga, P.Górka, P.Rybka, Bent rectangles as viscosity solutions over a circle, Nonlinear Analysis Series A: Theory, Methods and Applications, 125, (2015), 518-549. preprint
  23. Milena Matusik, Piotr Rybka, Oscillating facets, Port. Math. 73, (2016), 1-40 preprint
  24. Adam Kubica, Piotr Rybka, Fine singularity analysis of solutions to the Laplace equation, Math. Meth. Appl. Sci. 38 , (2015), 1734-1745, doi: 10.1002/mma.3182 preprint
  25. Piotr B. Mucha, Monika Muszkieta, Piotr Rybka, Two cases of squares evolving by anisotropic diffusion, Advances in Differential Equation, 20, (2015), 773-800. preprint.
  26. M. D. Korzec, P. Nayar and P. Rybka, Global attractors of sixth order PDEs describing the faceting of growing surfaces, Journal of Dynamics and Differential Equations, 28, (2016), 49-67, correction
  27. Piotr B. Mucha, Piotr Rybka, Well-posedness of sudden directional diffusion equations, Math. Meth. Appl. Sci. 36 , (2013), 2359-2370. preprint.
  28. Y. Giga, P.Górka, P.Rybka, Evolution of regular bent rectangles by the driven crystalline curvature flow in the plane with a non-uniform forcing term, Advances in Differential Equations 18, (2013), 201-242. preprint.
  29. M.H. Giga, Y. Giga, P.Rybka, A comparison principle for singular diffusion equations with spatially inhomogeneous driving force, Archive for Rational Mechanics and Analysis, 211, (2014), 419-453, DOI: 10.1007/s00205-013-0676-y, erratum
  30. Piotr B. Mucha, Piotr Rybka, A note on a model system with sudden directional diffusion, J. Statistical Physics, 146, (2012), 975-988, DOI:10.1007/s10955-012-0446-5.
  31. Karolina Kielak, Piotr B. Mucha, Piotr Rybka, Almost classical solutions to the total variation flow, J.Evolution Eqs, 13, (2013), 21-49
  32. M. Korzec, P. Rybka, On a higher order convective convective Cahn-Hilliard type equation, SIAM J. Appl. Math. 72, (2012), 1343-1360. preprint.
  33. M. Korzec, P. Nayar, P. Rybka, Global weak solutions to a sixth order Cahn-Hilliard type equation, SIAM J. Math. Analysis, 44, (2012), 3369-3387. preprint.
  34. Y. Giga, P.Górka, P.Rybka, A Comparison Principle for Hamilton-Jacobi equations with discontinuous Hamiltonians, Proc. AMS. 139, (2011), 1777-1785. (preprint.)
  35. 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
  36. P.Górka, P.Rybka, Existence and uniqueness of solutions to singular ODE's, Arch. Math., 94, (2010), 227-233.
  37. Y. Giga, P.Górka, P.Rybka, Nonlocal spatially inhomogeneous Hamilton-Jacobi equation with unusual free boundary, Discrete Contin. Dyn. Syst., 26, (2010), 493-519.
  38. 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.
  39. 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:
  40. P.B. Mucha, P.Rybka, A caricature of a singular curvature flow in the plane, Nonlinearity, 21, (2008), 2281-2316.
  41. 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.
  42. 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
  43. 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.
  44. 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.
  45. Y. Giga, P. Rybka, Stability of facets of crystals growing from vapor, Discrete Contin. Dyn. Syst. 14 (2006), no. 4, 689-706.
  46. Y. Giga, P.Rybka, Stability of facets of self-similar motion of a crystal, Advances in Differential Equation, 10, Number 6, (2005), 601-634.
  47. P. Rybka, M. Luskin, Existence of Energy Minimizers for Magnetostrictive Materials, SIAM J. Math. Anal. 36, No. 6, (2005) pp. 2004-2019.
  48. Y. Giga, P.Rybka, Existence of self-similar evolution of crystals grown from supersaturated vapor, Interfaces Free Bound. 6 (2004), 405-421.
  49. Y. Giga, P.Rybka, Berg's effect, Adv. Math. Sci. Appl., 13 no 2 (2003), 625-637.
  50. 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.
  51. P.Rybka, Q.Tang, D.Waxman, Evolution in a changing environment: Existence of Solutions, Coll. Math. 98, no 1 (2003).
  52. Y. Giga, P.Rybka, Quasi-static evolution of 3-D crystals grown from supersaturated vapor, Diff. Integral Equations. 15 no 1 (2002), 1-15.
  53. Y. Giga, M.Paolini, P.Rybka, On the motion by singular interfacial energy, Japan J. Indust. Appl. Math. 18, (2001), 231-248.
  54. P.Rybka, On modified crystalline Stefan problem with singular data, J.Differential Equations, 181, (2002), 340-366.
  55. 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.
  56. 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.
  57. P.Rybka and K.-H.Hoffmann, On convergence of solutions to the equation of viscoelasticity with capillarity, Commun. PDE., 25 (2000), 1845-1890.
  58. P.Rybka and K.-H.Hoffmann Convergence of solutions to Cahn-Hilliard equation, Commun. PDE. 24 (1999), 1055-1077.
  59. 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.
  60. 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
  61. P.Rybka Crystalline version of the Stefan problem with Gibbs-Thompson law and kinetic undercooling, Advances in Differential Equations, 3, (1998), 687-713.
  62. P.Rybka Viscous damping prevents propagation of singularities in the system of viscoelasticity, Proc. Royal Soc. Edinburgh A 127 (1997), 1067-1074.
  63. P.Rybka A crystalline motion: uniqueness and geometric properties, SIAM J. Appl. Math. 57 (1997), 53-72.
  64. P.Rybka A quasi-steady approximation to an integro-differential model of interface motion, Applicable Analysis 56 (1995), 19-34.
  65. 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.
  66. 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.
  67. P.Rybka Dynamical modeling of phase transitions by means of viscoelasticity in many dimensions, Proc. Royal Soc. Edinburgh A, 121, (1992), 101-138.
  68. P.Rybka, Propagation of weak singularities on characteristic surfaces of non-constant multiplicity, Ann. Polon. Math. 49, (1988), 82-92.
  69. 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. Atsushi Nakayasu, Piotr Rybka, Energy solutions to one-dimensional singular parabolic problems with BV data are viscosity solutions, in: "Mathematics for Nonlinear Phenomena - Analysis and Computation", In Honor of Professor Yoshikazu Giga's 60th birthday, ed. Y. Maekawa, Sh. Jimbo, Springer Proceedings in Mathematics and Statistics, 2017, 195-214. preprint
  2. Piotr B. Mucha, Piotr Rybka, Models of sudden directional diffusion, Advanced Studies in Pure Mathematics, 67 (2015) Variational Methods for Evolving Objects, 225-244.
  3. 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.
  4. 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
  5. 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
  6. P.Rybka, The modified crystalline Stefan problem: evolution of broken facets, Surikaisekikenkyusho Kokyuroku [RIMS Proceedings], No 1210 (2001) 142-155.
  7. 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.
  8. 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

  1. ``Variational Methods for Evolving Objects", Eds: Luigi Ambrosio, Yoshikazu Giga, Piotr Rybka, Yoshihiro Tonegawa, Advanced Studies in Pure Mathematics, 67, Mathematical Society of Japan, 2015
  2. ``Nonlocal and Abstract Parabolic Equations and their Applications", Eds: Piotr Mucha, Marek Niezgódka and Piotr Rybka, Banach Center Publ. 86, IMPAN, Warszawa, 2009

Textbooks

  1. M.Borodzik, P.Goldstein, P.Rybka, A.Zatorska-Goldstein, Problems on Partial Differential Equations, table of content, Springer, Cham, 2019.
  2. Piotr Rybka, The BV space in variational and evolution problems, Lecture Notes, Nov. 1 -- Nov. 10, 2016, The University of Tokyo.
  3. "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.
  4. Piotr Rybka, Mathematics for chemistry students, (in Polish) lecture notes set for course Mathematics B, given at the Chemistry Faculty, the University of Warsaw, 2002.

Piotr Rybka