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Peer Reviewed Journal Articles

Allen, H.R., Ptashnyk, M.
Mathematical modelling and analysis of the Brassinosteroid and Gibberellin signalling pathways and their interactions,
arXiv:1703.07584, 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., 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.
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, in press, 2016. [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

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]
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