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Research Publications Teaching Minisymposia Talks Home

Peer Reviewed Journal Articles

King J.R., Köry J., Ptashnyk M.
Multiscale analysis of nutrient uptake by plant root hairs with sparse distribution of hairs: Nonstandard scaling,
SIAM J Applied Mathematics, in press, 2021, arXiv:1911.06293 [Link]
Daus E., Ptashnyk M., Raithel C.
Derivation of a fractional cross-diffusion system as the limit of a stochastic many-particle system driven by Lévy noise,
arXiv:2006.00277, 2020 [Link]
Piatnitski, A., Ptashnyk, M.
Homogenization of biomechanical models of plant tissues with randomly distributed cells,
Nonlinearity, 33, 5510-5542, 2020 [Link]
Lorenzi, T., Murray, P., Ptashnyk, M.
From individual-based mechanical models of multicellular systems to free-boundary problems,
Interace and Free Boundary, 22, 205-244, 2020 [Link] [PDF] arXiv:1903.06590 [Link]
Ptashnyk, M., Venkataraman C.
Multiscale analysis and simulation of a signalling process with surface diffusion,
Multiscale Modelling and Simulation, SIAM Journal, 2020, 18, 851-886 [Link] [PDF]
Athanassoulis A., Athanassoulis G., Ptashnyk M., Sapsis T.
Strong solutions for the Alber equation and stability of unidirectional wave spectra,
Kinetic and Related Models, 13, 703-737, 2020 [Link] [PDF]
Allen, H.R., Ptashnyk, M.
Mathematical Modelling of Auxin Transport in Plant Tissues: Flux meets Signalling and Growth,
Bulletin of Mathematical Biology, 82, 17, 2020 [Link]
Juengel, A., Ptashnyk, M.
Homogenization of degenerate cross-diffusion systems,
J Differential Equations, 2019 [Link] [PDF]
Mimault M., Ptashnyk M., Bassel G.W., Dupuy L.X.
Smoothed particle hydrodynamics for root growth mechanics,
Engineering Analysis with Boundary Elements, 105, 20-30, 2019 [Link]
Ptashnyk M.
Homogenization of some degenerate pseudoparabolic variational inequalities,
Journal of Mathematical Analysis and Applications, 469, 44-75, 2019 [Link] [PDF]
Dupuy L.X., Mimault M., Patko D., Ladmiral V., Ameduri B., MacDonald M.P., Ptashnyk M.
Micromechanics of root development in soil,
Current Opinion in Genetics and Development, 51, 18-25, 2018. [Link]
De La Fuente Canto C., Kalogiros D.I., Ptashnyk M., George T.S., Waugh R., Bengough A.G., Russell J., Dupuy L.X.
Morphological and genetic characterisation of the root system architecture of selected barley Recombinant Chromosome Substitution Lines using an integrated phenotyping pipeline,
Journal of Theoretical Biology, 447, 84-97, 2018. [Link]
Allen, H.R., Ptashnyk, M.
Mathematical modelling and analysis of the Brassinosteroid and Gibberellin signalling pathways and their interactions,
Journal of Theoretical Biology, 432, 109-131, 2017 [Link]
Piatnitski, A., Ptashnyk, M.
Homogenization of biomechanical models for plant tissues,
Multiscale Modelling and Simulations, SIAM Journal, 15, 339-387, 2017 [Link]
Ptashnyk, M.
Multiscale modelling and analysis of signalling processes in tissues with non-periodic distribution of cells,
Vietnam Journal of Mathematics, 45, 295-316, 2017 . [Link]
Ptashnyk, M., Seguin, B.
Homogenization of a viscoelastic model for plant cell wall biomechanics,
ESAIM: Control, Optimis., Calculus of Variations, 23, 1447-1471, 2017 [Link]
Ptashnyk, M., Seguin, B.
Multiscale analysis of a system of elastic and reaction-diffusion equations modelling plant cell wall biomechanics, ESAIM M2AN, 50, 593-631, 2016 [Link] arXiv:1410.6911 [Link]
Ptashnyk, M., Seguin, B.
The impact of microfibril orientations on the biomechanics of plant cell walls and tissues: modelling and simulations,
Bulletin of Mathematical Biology, 78, 2135-2164, 2016. [Link]
Matzavinos, A., Ptashnyk, M.
Stochastic homogenization of the Keller–Segel chemotaxis system,
Nonlinear Analysis: Theory, Methods and Applications, 144, 58-76, 2016. [Link] [PDF]
Kalogiros D.I., Adu M.O., White P.J., Broadley M.R., Draye X., Ptashnyk M., Bengough A.G., Dupuy L.X.
Analysis of root growth from a phenotyping dataset using a density-based model,
J Experimental Botany, 67, 1045-1058, 2016 [Link]
Ptashnyk, M., Seguin, B.
Periodic homogenization and material symmetry in linear elasticity,
Journal of Elasticity, 124, 225-241, 2016. [Link] arXiv:1504.08165 [Link]
Medkova, D., Ptashnyk, M., Varnhorn, W.
Generalized Darcy-Oseen resolvent problem,
Mathematical Methods in Applied Sciences, 39, 1621-1630, 2016 [Link] [PDF]
Ptashnyk, M.
Locally periodic unfolding method and two-scale convergence on surfaces of locally periodic microstructures,
Multiscale Modelling and Simulations, SIAM Journal, 13, 1061-1105, 2015. [Link]
Matzavinos, A., Ptashnyk, M.
Homogenization of oxygen transport in biological tissues, Applicable Analysis, 2015. [Link] [Link]
Chaplain, M., Ptashnyk, M., Sturrock, M.
Hopf bifurcation in a gene regulatory network model: Molecular movement causes oscillations,
Mathematical Models and Methods in Applied Sciences , 25, 1179-1215, 2015. [Link] [PDF]
Medkova, D., Ptashnyk, M., Varnhorn, W.
Integral representation of a solution to the Stokes-Darcy problem,
Mathematical Methods in Applied Sciences, 38, 3968-3979, 2015. [PDF]
Claus, J., Ptashnyk, M., Bohmann, A., Chavarría-Krauser, A.
Global Hopf Bifurcation in the ZIP regulatory system, J Mathematical Biology, 71, 795-816, 2015. [Link]
Chavarría-Krauser, A., Ptashnyk, M.
Homogenization approach to water transport in plant tissues with periodic microstructures.
Mathematical Modelling of Natural Phenomena, 8, 80-111, 2013. [Link] [PDF]
Melcher, C., Ptashnyk, M.
Landau-Lifshitz-Slonczewski equations: Global weak and classical solutions.
SIAM J Mathematical Analysis , 45, 407-429, 2013. [Link] [PDF]
Ptashnyk, M.
Two-scale convergence for locally-periodic microstructures and homogenization of plywood structures.
Multiscale Modelling and Simulations, SIAM J, 11, 92-117, 2013. [Link] [PDF]
Mercker, M., Ptashnyk, M., Kühnle, J., Hartmann, D., Weiss, M., Jäger, W.
A multiscale and multidisciplinary approach to curvature modulated sorting in biological membranes.
J Theoretical Biology, 301, 67-82, 2012. [Link] [PDF]
Golovaty, Y., Marciniak-Czochra, A., Ptashnyk, M.
Stability of nonconstant stationary solu- tions in a reaction-diffusion equation coupled to the system of ordinary differential equations. Communications on Pure and Applied Analysis, 11, 229-241, 2012. [Link]
Fatima, T., Muntean, A., Ptashnyk, M.
Error estimate and unfolding method for homogenization of a reaction-diffusion system modeling sulfate corrosion. Applicable Analysis, 91, 1129-1154, 2012. [Link] [PDF]
Capdeboscq, Y., Ptashnyk, M.
Root growth: Homogenization in domain with time dependent partial perforation,
ESAIM: Control, Optimisation and Calculus of Variations, online, 18, 856-876, 2012. [Link] [PDF]
Ptashnyk, M., Roose, T., Jones, D.L., Kirk, G.J.D.
Enhanced zinc uptake by rice by phytosiderophore secretion: a modelling study,
Plant, Cell and Environment, 34, 2038-2046, 2011. [Link][PDF]
Ptashnyk, M., Roose, T., Kirk, G.
Diffusion of strongly sorbed solutes in soil: a dual-porosity model allowing for slow access to sorption sites and time-dependent sorption reactions. EJSS, 61, 108-119, 2010 [Link][PDF]
Ptashnyk, M., Roose, T.
Derivation of a macroscopic model for transport of strongly sorbed solutes in the soil using homogenization theory. SIAM J Appl Math, 70, 2097-2118, 2010. [Link] [PDF]
Leitner, D., Klepsch, S., Ptashnyk, M., Marchant, A., Kirk, G., Schnepf, A., Roose, T.
A dynamic model of nutrient uptake by root hairs based on homogenisation.
New Phytologist, 185, 792-802, 2010. [Link][PDF]
Chavarría-Krauser, A., Ptashnyk, M.
Homogenization of long-range auxin transport in plant tissues.
Nonlinear Analysis: Real World Applications, 11, 4524-4532, 2010. [Link] [PDF]
Ptashnyk, M.
Derivation of a macroscopic model for nutrient uptake by a single branch of hairy-roots.
Nonlinear Analysis: Real World Applications, 11, 4586-4596, 2010. [Link][PDF]
Marciniak-Czochra, A., Ptashnyk, M.
Boundedness of solutions of a haptotaxis model.
M3AS: Mathematical Models and Methods in Applied Sciences, 20, 449-476, 2010. [Link] [PDF]
Bastian, P., Chavarria-Krauser, A., Engwer, C., Jäger, W., Marnach, S., Ptashnyk, M.
Modeling in vitro growth of dense root network. J Theoretical Biology, 254 (1), 99-109, 2008. [Link][PDF]
Marciniak-Czochra, A., Ptashnyk, M.
Derivation of a macroscopic receptor-based model using homogenization techniques.
SIAM J. Math Anal, 40 (1), 215-237, 2008. [Link] [PDF]
Ptashnyk, M.
Pseudoparabolic equations with convection. IMA J. Applied Mathematics, 72 (6), 2007. [Link][PDF]
Ptashnyk, M.
Degenerate quasilinear pseudoparabolic equations with memory terms and variational inequalities.
Nonlinear Analysis, Theory, Methods, Applications, 66 (12), 2653-2675, 2006. [Link][PDF]
Ptashnyk, M.
Nonlinear pseudoparabolic equations as singular limit of reaction-diffusion equations.
Applicable Analysis, 85 (10), 1285-1299, 2006. [Link][PDF]
Ptashnyk, M.
Some pseudoparabolic variational inequalities with higher order derivatives.
Ukrainian Mathematical Journal, 54 (1), 112-125, 2002.[PDF]
Lavrenyuk, S., Ptashnyk, M.
Problem without initial conditions for a nonlinear pseudoparabolic system.
Differential Equations, 36 (5), 739-748, 2000.
Lavrenyuk, S., Ptashnyk, M.
On certain nonlinear pseudoparabolic variational inequalities without initial conditions.
Ukrainian Mathematical Journal, 51 (3), 366-376, 1999.[PDF]
Lavrenyuk, S., Ptashnyk, M.
Pseudo-parabolic variational inequalities without initial conditions.
Ukrainian Mathematical Journal, 50 (7), 1045-1057, 1998.[PDF]

Invited chapters in books

Ptashnyk, M., Allen, H.R.
Calcium-Pectin Chemistry and Biomechanics: Biological Background and Mathematical Modelling,
Plant Biomechanics, A. Geitmann, J. Gril, Editors, Springer, 273-303, 2018 [Link]
Bastian, P., Bauer, J., Chavarría-Krauser, A., Engwer, C., Jäger, W., Marnach, S., Ptashnyk, M., Wetterauer, B.
Modeling and Simulation of Hairy Root Growth.
Mathematics--Key Technology for the Future, 101-115, 2008. [Link] [PDF]

PhD thesis

Ptashnyk, M. Nonlinear Pseudoparabolic Equations and Variational Inequalities.
SFB-Preprint, University of Heidelberg, 2004. [PDF]