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Publications
Piotr Rybka
Number of publications: 622022
- Tokinaga Namba, Piotr Rybka , Shoichi Sato, Special solutions to the space fractional diffusion problem, FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 25 (6) 2022, p. 2139-2165. See in PBN
- Piotr Rybka , Ahmad Sabra, The planar Least Gradient problem in convex domains, the case of continuous datum, Nonlinear Analysis, 214 2022, p. 112595: 1-27. See in PBN
2021
- Michał Łasica , Piotr Rybka , Existence of W^{1,1} solutions to a class of variational problems with linear growth on convex domains, Indiana University Mathematics Journal, 70 (6) 2021, p. 2427-2450. See in PBN
- Tokinaga Namba, Piotr Rybka , Vaughan Voller, Some comments on using fractional derivative operators in modeling non-local diffusion processes, Journal of Computational and Applied Mathematics, 381 2021, p. 113040, 1-17. See in PBN
- Piotr Rybka , Ahmad Sabra, The planar least gradient problem in convex domains: the discontinuous case, Nonlinear Differential Equations and Applications, 28 (2) 2021. See in PBN
2020
- Piotr Rybka , Anna Zatorska-Goldstein , A stationary heat conduction problem in low dimensional sets in R^N, Calculus of Variations and Partial Differential Equations, 59 (1) 2020, p. 1-24. See in PBN
- M. D. Korzec, Piotr Nayar , Piotr Rybka , Correction to: Global Attractors of Sixth Order PDEs Describing the Faceting of Growing Surfaces, Journal of Dynamics and Differential Equations, 32 (3) 2020, p. 1577-1578. See in PBN
- 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 (12) 2020, p. 10587-10629. See in PBN
- Tokinaga Namba, Piotr Rybka , On Viscosity Solutions of Space-Fractional Diffusion Equations of Caputo Type, SIAM Journal on Mathematical Analysis, 52 (1) 2020, p. 653-681. See in PBN
2019
- Yoshikazu Giga, Monika Muszkieta, Piotr Rybka , A duality based approach to the minimizing total variation flow in the space $H^{-s}$, Japan Journal of Industrial and Applied Mathematics, 36 (1) 2019, p. 261–286. See in PBN
- Maciej Borodzik , Paweł Goldstein , Piotr Rybka , Anna Zatorska-Goldstein , Problems on Partial Differential Equations, 2019. See in PBN
2018
- Atsushi Nakayasu, Piotr Rybka , Integrability of the derivative of solutions to a singular one-dimensional parabolic problem, Topological Methods in Nonlinear Analysis, 52 (1) 2018, p. 239-257. See in PBN
2017
- Atsushi Nakayasu, Piotr Rybka , Energy Solutions to One-Dimensional Singular Parabolic Problems with \$\$\ BV\$\$ Data are Viscosity Solutions, Mathematics for Nonlinear Phenomena --- Analysis and Computation: In Honor of Yoshikazu Giga's 60th Birthday, Sapporo, Japan, August 2015, 2017, p. 195-213. See in PBN
- Piotr Rybka , Ahmad Sabra, Wojciech Górny, Special cases of the planar least gradient problem, Nonlinear Analysis, Theory, Methods and Applications, 151 2017, p. 66-95. See in PBN
- Adam Kubica, Piotr Rybka , K. Ryszewska, Weak solutions of fractional differential equations in non cylindrical domains, NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 36 2017, p. 154-18. See in PBN
2016
- Adam Kubica, Piotr Rybka , Fine singularity analysis of solutions to the Laplace equation: Berg's effect, Mathematical Methods in the Applied Sciences, 2016. See in PBN
- Piotr Rybka , M. D. Korzec, P. Nayar, Global attractors of sixth order PDEs describing the faceting of growing surfaces, Journal of Dynamics and Differential Equations, 28 (1) 2016, p. 49-67. See in PBN
- Milena Matusik, Piotr Rybka , Oscillating facets, Portugaliae Mathematica, 2016. See in PBN
2015
- Yoshikazu Giga, Przemysław Górka, Piotr Rybka , Bent rectangles as viscosity solutions over a circle, Nonlinear Analysis, Theory, Methods and Applications, 2015. See in PBN
- Adam Kubica, Piotr Rybka , Fine singularity analysis of solutions to the Laplace equation, Mathematical Methods in the Applied Sciences, 2015. See in PBN
- Piotr Mucha , Piotr Rybka , Models of sudden directional diffusion, Variational Methods for Evolving Objects, Sapporo, Japan, 30 July 2012 - 3 August 2012. See in PBN
- Piotr Mucha , Monika Muszkieta, Piotr Rybka , Two cases of squares evolving by anisotropic diffusion, Advances in Differential Equations, 20 2015, p. 773-800. See in PBN
- Luigi Ambrosio, Yoshikazu Giga, Piotr Rybka , Yoshihiro Tonegawa, Variational Methods for Evolving Objects, Variational Methods for Evolving Objects, Sapporo, Japan, 30 July 2012 - 3 August 2012. See in PBN
2014
- M.-H. Giga, Y. Giga, Piotr Rybka , A comparison principle for singular diffusion equations with spatially inhomogeneous driving force for graphs, Archive for Rational Mechanics and Analysis, 2014. See in PBN
- Piotr Rybka , - M. -H. Giga, - Y. Giga, Erratum to: A Comparison Principle for Singular Diffusion Equations with Spatially Inhomogeneous Driving Force for Graphs, Archive for Rational Mechanics and Analysis, 212 (2) 2014, p. 707-707. See in PBN
2013
- Piotr Mucha , Piotr Rybka , Karolina Kielak, Almost classical solutions to the total variation flow, Journal of Evolution Equations, 13 2013, p. 21-49. See in PBN
- Piotr Rybka , Yoshikazu Giga, Przemysław Górka, 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 (3-4) 2013, p. 201-242. See in PBN
- Piotr Mucha , Piotr Rybka , Well posedness of sudden directional diffusion equations, Mathematical Methods in the Applied Sciences, 2013. See in PBN
- Piotr Mucha , Piotr Rybka , Well-posedness of sudden directional diffusion equations, Mathematical Methods in the Applied Sciences, 2013. See in PBN
2012
- Piotr Mucha , Piotr Rybka , A Note on a Model System with Sudden Directional Diffusion, Journal of Statistical Physics, 2012. See in PBN
- Maciej D. Korzec, Piotr Nayar , Piotr Rybka , Global Weak Solutions to a Sixth Order Cahn-Hilliard Type Equation, SIAM Journal on Mathematical Analysis, 2012. See in PBN
- M. Korzec, Piotr Rybka , On a higher order convective Cahn-Hilliard-type equation, SIAM Journal on Applied Mathematics, 2012. See in PBN
2011
- Yoshikazu Giga, Przemysław Górka, Piotr Rybka , A comparison principle for Hamilton-Jacobi equations with discontinuous Hamiltonians, Proceedings of the American Mathematical Society, 2011. See in PBN
2010
- Przemysław Górka, Piotr Rybka , Existence and uniqueness of solutions to singular ODE's, Archiv der Mathematik, 2010. See in PBN
- Yoshikazu Giga, Przemysław Górka, Piotr Rybka , Nonlocal spatially inhomogeneous Hamilton-Jacobi equation with unusual free boundary, Discrete and Continuous Dynamical Systems, 2010. See in PBN
- Danielle Hilhorst, Piotr Rybka , Stabilization of Solutions to a FitzHugh-Nagumo Type System, Journal of Statistical Physics, 2010. See in PBN
- W. Merz, Piotr Rybka , Strong solutions to the Richards equation in the unsaturated zone, Journal of Mathematical Analysis and Applications, 2010. See in PBN
2009
- Piotr Mucha , Piotr Rybka , Almost classical solutions of static Stefan type problems involving crystalline curvature, Nonlocal and Abstract Parabolic Equations and their Applications, 2009. See in PBN
- Yoshikazu Giga, Piotr Rybka , Facet bending driven by the planar crystalline curvature with a generic nonuniform forcing term, Journal of Differential Equations, 2009. See in PBN
- Piotr Mucha , Marek Niezgódka, Piotr Rybka , Nonlocal and Abstract Parabolic Equations and their Applications, 2009. See in PBN
2008
- Piotr Mucha , Piotr Rybka , A caricature of a singular flow in the plane, Nonlinearity, 2008. See in PBN
- Yoshikazu Giga, Piotr Rybka , Etsuro Yokoyama, A microscopic time scale approximation to the behavior of the local slope on the faceted surface under a nonuniformity in supersayuration, Physica D: Nonlinear Phenomena, 2008. See in PBN
- Yoshikazu Giga, Piotr Rybka , Facet bending in the driven crystalline curvature flow in the plane, Journal of Geometric Analysis, 2008. See in PBN
- Yoshikazu Giga, Piotr Rybka , Faceted crystals grow from solutions - a Stefan type problem with a singular interfacial energy, 2008. See in PBN
2007
- Piotr Mucha , Piotr Rybka , A new look at equilibrium in Stefan-type problems in the plane, SIAM Journal on Mathematical Analysis, 2007. See in PBN
2006
- Piotr Rybka , Convergence of a heat flow on a Hilbert manifold, Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 2006. See in PBN
- Yoshikazu Giga, Piotr Rybka , Stability of facets of crystals growing from vapor, Discrete and Continuous Dynamical Systems, 2006. See in PBN
2005
- Yoshikazu Giga, Piotr Rybka , A Stefan type problem arising in modeling ice crystals growing from vapor, 2005. See in PBN
- Mitchell Luskin, Piotr Rybka , Existence of energy minimizers for magnetostrictive materials, SIAM Journal on Mathematical Analysis, 2005. See in PBN
- Yoshikazu Giga, Piotr Rybka , Stability of facets of self-similar motion of a crystal, Advances in Differential Equations, 2005. See in PBN
2004
- W Merz, Piotr Rybka , A free boundary problem describing reaction-diffusion problems in chemical vapor infiltration of pyrolytic carbon, Journal of Mathematical Analysis and Applications, 2004. See in PBN
- Yoshikazu Giga, Piotr Rybka , Existence of self-similar evolution of crystals grown from supersaturated vapor, Interfaces and Free Boundaries, 2004. See in PBN
2003
- Y Giga, Piotr Rybka , Bergs effect, Advances in Mathematical Sciences and Applications, 2003. See in PBN
- Piotr Rybka , Q Tang, D Waxman, Evolution in a changing environment: Existence of solutions, Colloquium Mathematicum, 2003. See in PBN
2002
- K Hoffmann, Piotr Rybka , Analyticity of the nonlinear term forces convergence of solutions to two equations of continuum mechanics., Nonlinear Analysis, Theory, Methods and Applications, 2002. See in PBN
- Piotr Rybka , On modified crystalline Stefan problem with singular data., Journal of Differential Equations, 2002. See in PBN
- Y Giga, Piotr Rybka , Quasi-static evolution of 3-D crystals grown from supersaturated vapor., Differential and Integral Equations, 2002. See in PBN
2001
- Yoshikazu Giga, Maurizio Paolini, Piotr Rybka , On the motion by singular interfacial energy., Japan Journal of Industrial and Applied Mathematics, 2001. See in PBN
- Piotr Rybka , The modified crystalline Stefan problem: evolution of broken facets., 2001. See in PBN
2000
- Piotr Rybka , On convergence of solutions of the crystalline Stefan problem with Gibbs-Thomson law and kinetic undercooling., Interfaces and Free Boundaries, 2000. See in PBN
- Karl-Heinz Hoffmann, Piotr Rybka , On convergence of solutions to the equation of viscoelasticity with capillarity., Communications in Partial Differential Equations, 2000. See in PBN
Others
- Atsushi Nakayasu, Piotr Rybka , Energy Solutions to One-Dimensional Singular Parabolic Problems with $${ BV}$$ Data are Viscosity Solutions, Mathematics for Nonlinear Phenomena --- Analysis and Computation: In Honor of Yoshikazu Giga's 60th Birthday, Sapporo, Japan, August 2015, , p. 195-213. See in PBN