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- Anna Marciniak-Czochra, Mariya Ptashnyk
- SIAM J. Math. Analysis
- 2008

- Mariya Ptashnyk
- Multiscale Modeling & Simulation
- 2013

Abstract. The introduced notion of locally periodic two-scale convergence allows one to average a wider range of microstructures, compared to the periodic one. The compactness theorem for locally periodic two-scale convergence and the characterization of the limit for a sequence bounded in H1(Î©) are proven. The underlying analysis comprises theâ€¦ (More)

- Mariya Ptashnyk, Tiina Roose, Davey L. Jones, Guy J D Kirk
- Plant, cell & environment
- 2011

Rice (Oryza sativa L.) secretes far smaller amounts of metal-complexing phytosiderophores (PS) than other grasses. But there is increasing evidence that it relies on PS secretion for its zinc (Zn) uptake. After nitrogen, Zn deficiency is the most common nutrient disorder in rice, affecting up to 50% of lowland rice soils globally. We developed aâ€¦ (More)

- Christof Melcher, Mariya Ptashnyk
- SIAM J. Math. Analysis
- 2013

We consider magnetization dynamics under the influence of a spin-polarized current, given in terms of a spin-velocity field v, governed by the following modification of the Landauâ€“ Lifshitzâ€“Gilbert equation âˆ‚m âˆ‚t + v Â· âˆ‡m = m Ã— (Î± âˆ‚m âˆ‚t + Î² v Â· âˆ‡m âˆ’ Î”m), called the Landauâ€“ Lifshitzâ€“Slonczewski equation. We focus on the situation of magnetizations defined onâ€¦ (More)

Abstract In this paper, we focus on the one-dimensional Keller-Segel chemotaxis system in a random heterogeneous domain. We assume that the corresponding diffusion and chemotaxis coefficients are given by stationary ergodic processes, and apply methods pertaining to stochastic two-scale convergence to derive the homogenized macroscopic equations. Specialâ€¦ (More)

- Mariya Ptashnyk, Tiina Roose
- SIAM Journal of Applied Mathematics
- 2010

Abstract. In this paper we derive a model for the diffusion of strongly sorbed solutes in soil taking into account diffusion within both the soil fluid phase and the soil particles. The model takes into account the effect of solutes being bound to soil particle surfaces by a reversible nonlinear reaction. Effective macroscale equations for the soluteâ€¦ (More)

We use the periodic unfolding technique to derive corrector estimates for a reaction-diffusion system describing concrete corrosion penetration in the sewer pipes. The system, defined in a periodically-perforated domain, is semi-linear, partially dissipative, and coupled via a non-linear ordinary differential equation posed on the solid-water interface atâ€¦ (More)

With methods of potential theory we develop a representation of the solution of a coupled Stokes-Darcy model in a Lipschitz domain for boundary data in Hâˆ’1/2.

- Andrey L. Piatnitski, Mariya Ptashnyk
- Multiscale Modeling & Simulation
- 2017

- Mariya Ptashnyk
- Multiscale Modeling & Simulation
- 2015

In this paper we generalize the periodic unfolding method and the notion of twoscale convergence on surfaces of periodic microstructures to locally periodic situations. The methods that we introduce allow us to consider a wide range of nonperiodic microstructures, especially to derive macroscopic equations for problems posed in domains with perforationsâ€¦ (More)