Dr Mariya Ptashnyk

Name:

Mariya Ptashnyk

Position:

Lecturer

Address:

Department of Mathematics

University of Dundee

Dundee DD1 4HN

Room:

2.47

E-mail:

mptashnykmaths.dundee.ac.uk

Phone:

+44 1382 384467

Fax:

+44 1382 385516

Research Interests:

• nonlinear partial differential equations
• multiscale modelling and analysis

Mathematical Biology:

• growth of plant roots
• transport processes in plant roots
• soil-roots interaction
• receptor-based models for cell signalling

Civil Engineering:

• microscopic structure of concrete
• concrete corrosion

Editorial:

Editorial board for a special issue on 'Analysis and Approximation of Miscrostructure Models' in the journal "Applicable Analysis", 2012.

Editorial board for a special issue on 'Plant modelling' in the journal "Mathematical modelling of natural phenomena", to appear in 2013.

Publications:

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, online, 2012.

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.

Fatima, T., Muntean, A., Ptashnyk, M.

Error estimate and unfolding method for homogeniza- tion of a reaction-diffusion system modeling sulfate corrosion. Applicable Analysis, online, 2011.

Capdeboscq, Y., Ptashnyk, M.

Root growth: Homogenization in domain with time dependent partial perforation,
ESAIM: Control, Optimisation and Calculus of Variations, online, 2011.

Ptashnyk, M., Roose, T., Kirk, G.

Model of diffusion of strongly-sorbed solutes through soil allowing for slow access to and from sorption sites and time-dependent sorption reactions. EJSS, 61, 108-119, 2010

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.

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.

Moritsuka, N., Ptashnyk, M., Roose, T., Jones, D.L., Kirk, G.J.D.

Diffusion of strongly-sorbed solutes in soil: experimental testing of a dual porosity model. submitted to EJSS, 2009.

Chavarría-Krauser, A., Ptashnyk, M.

Homogenization of long-range auxin transport in plant tissues.
Nonlinear Analysis: Real World Applications, 11, 4524-4532, 2010.

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.

Marciniak-Czochra, A., Ptashnyk, M.

Boundedness of solutions of a haptotaxis model.
M3AS: Mathematical Models and Methods in Applied Sciences, 20, 449-476, 2010.

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.

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.

Marciniak-Czochra, A., Ptashnyk, M.

Derivation of a macroscopic receptor-based model using homogenization techniques.
SIAM J. Math Anal, 40 (1), 215-237, 2008.

Ptashnyk, M.

Pseudoparabolic equations with convection. IMA J. Applied Mathematics, 72 (6), 2007.

Ptashnyk, M.

Degenerate quasilinear pseudoparabolic equations with memory terms and variational inequalities.
Nonlinear Analysis, Theory, Methods, Applications, 66 (12), 2653-2675, 2006.

Ptashnyk, M.

Nonlinear pseudoparabolic equations as singular limit of reaction-diffusion equations.
Applicable Analysis, 85 (10), 1285-1299, 2006.

Ptashnyk, M.

Nonlinear Pseudoparabolic Equations and Variational Inequalities.
SFB-Preprint, University of Heidelberg, 2004.

Ptashnyk, M.

Some pseudoparabolic variational inequalities with higher order derivatives.
Ukrainian Mathematical Journal, 54 (1), 112-125, 2002.

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.

Lavrenyuk, S., Ptashnyk, M.

Pseudo-parabolic variational inequalities without initial conditions.
Ukrainian Mathematical Journal, 50 (7), 1045-1057, 1998.