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.
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
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
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
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
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
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
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
Piotr B. Mucha, Piotr Rybka,
Well-posedness of sudden directional diffusion equations,
Math. Meth. Appl. Sci. 36 , (2013), 2359-2370.
preprint.
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.
M. Korzec, P. Rybka,
On a higher order convective convective Cahn-Hilliard type
equation, SIAM J. Appl. Math. 72, (2012), 1343-1360.
preprint.
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.
Y. Giga, P.Górka, P.Rybka, A Comparison Principle for
Hamilton-Jacobi equations with discontinuous Hamiltonians,
Proc. AMS. 139, (2011), 1777-1785.
(preprint.)
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
P.Górka, P.Rybka, Existence and uniqueness of solutions to
singular ODE's, Arch. Math., 94, (2010), 227-233.
Y. Giga, P.Górka, P.Rybka, Nonlocal spatially
inhomogeneous Hamilton-Jacobi equation with unusual free boundary,
Discrete Contin. Dyn. Syst., 26, (2010), 493-519.
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.
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
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.
P. Rybka, M. Luskin, Existence of Energy Minimizers for
Magnetostrictive Materials, SIAM J. Math. Anal. 36, No. 6, (2005) pp. 2004-2019.
Y. Giga, P.Rybka, Existence of self-similar evolution of
crystals grown from supersaturated vapor, Interfaces Free Bound. 6 (2004), 405-421.
Y. Giga, P.Rybka, Berg's effect, Adv. Math.
Sci. Appl., 13 no 2 (2003), 625-637.
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.
P.Rybka, Q.Tang, D.Waxman, Evolution in a changing environment:
Existence of Solutions, Coll. Math. 98, no 1 (2003).
Y. Giga, M.Paolini, P.Rybka, On the motion by singular
interfacial energy, Japan J. Indust. Appl. Math. 18, (2001), 231-248.
P.Rybka, On modified crystalline Stefan problem with
singular data,
J.Differential Equations, 181, (2002), 340-366.
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.
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.
P.Rybka and K.-H.Hoffmann, On convergence of solutions to the equation
of viscoelasticity with capillarity, Commun. PDE., 25 (2000), 1845-1890.
P.Rybka and K.-H.Hoffmann Convergence of solutions to Cahn-Hilliard
equation, Commun. PDE. 24 (1999), 1055-1077.
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.
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
P.Rybka Viscous damping prevents propagation of
singularities in the
system of viscoelasticity, Proc. Royal Soc. Edinburgh A 127 (1997), 1067-1074.
P.Rybka A crystalline motion: uniqueness and geometric properties,
SIAM J. Appl. Math. 57 (1997), 53-72.
P.Rybka A quasi-steady approximation to an
integro-differential model of interface motion,
Applicable Analysis 56 (1995), 19-34.
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.
I.Fonseca, P.Rybka Relaxation of multiple integrals in the
space , Proc. Royal Soc. Edinburgh A, 121,
(1992), 321-348.
P.Rybka Dynamical modeling of phase transitions by means
of viscoelasticity in many dimensions, Proc. Royal Soc. Edinburgh A,
121, (1992), 101-138.
P.Rybka, Propagation of weak singularities on
characteristic surfaces of non-constant multiplicity, Ann. Polon. Math.
49, (1988), 82-92.
P.Rybka, The behaviour of weak singularities on
characteristic surfaces with multiplicity change, Bull. Polish Acad. Sci.
Math. 32, (1984), 675-679.
Piotr B. Mucha, Piotr Rybka,
Models of sudden directional diffusion, Advanced Studies in Pure Mathematics, 67
(2015) Variational Methods for Evolving Objects, 225-244.
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.
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
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
P.Rybka, The modified crystalline Stefan problem: evolution of broken
facets, Surikaisekikenkyusho Kokyuroku [RIMS Proceedings], No 1210 (2001)
142-155.
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.
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
``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
``Nonlocal and Abstract Parabolic Equations and their Applications",
Eds: Piotr Mucha, Marek Niezgódka and Piotr Rybka,
Banach Center Publ. 86, IMPAN, Warszawa, 2009
"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,
Mathematics for chemistry students,
(in Polish) lecture notes set
for course Mathematics B,
given at the Chemistry Faculty, the University of Warsaw, 2002.