Papers by Marek Niezgódka
Local existence and uniqueness of solutions to one-dimensional tumor invasion model
In the present paper, we propose a modified tumor invasion model which was originally proposed in... more In the present paper, we propose a modified tumor invasion model which was originally proposed in Chaplain and Anderson (2003) [1]. And we show the local existence and uniqueness of solutions to approximate systems of the 1D modified tumor invasion model. Especially, we introduce a new function and show that our system is equivalent to the nonlinear second-order PDE, which
Local existence and uniqueness of solutions to approximate systems of 1D tumor invasion model
Nonlinear Analysis-real World Applications, Oct 1, 2010
In the present paper, we propose a modified tumor invasion model which was originally proposed in... more In the present paper, we propose a modified tumor invasion model which was originally proposed in Chaplain and Anderson (2003) [1]. And we show the local existence and uniqueness of solutions to approximate systems of the 1D modified tumor invasion model. Especially, we introduce a new function and show that our system is equivalent to the nonlinear second-order PDE, which
Nonlinear Analysis-theory Methods & Applications, 1990
Addison Wesley Longman eBooks, 1996
Nonlinear analysis and applications : the proceedings of Banach Center Minisemester
Gakkōtosho eBooks, 1995
Localization of structural differences between serum and colostral ovine and bovine IgG1 and IgG2 immunoglobulins
Archivum immunologiae et therapiae experimentalis, 1978
Physicochemical and serological studies on immunoglobulins, their Fab and Fc fragments, L and H c... more Physicochemical and serological studies on immunoglobulins, their Fab and Fc fragments, L and H chains, showed that the strongest differences occurred in case of IgG2, and that the differences were localized in the Fc region.
The Stefan Problem
The Stefan Problem, 1992
The Stefan Problem (Kirchen Der Welt
arXiv (Cornell University), Mar 13, 2017
We perform mathematical anaysis of the biofilm development process. A model describing biomass gr... more We perform mathematical anaysis of the biofilm development process. A model describing biomass growth is proposed: It arises from coupling three parabolic nonlinear equations: a biomass equation with degenerate and singular diffusion, a nutrient tranport equation with a biomass-density dependent diffusion, and an equation of the Navier-Stokes type, describing the fluid flow in which the biofilm develops. This flow is subject to a biomass-density dependent obstacle. The model is treated as a system of three inclusions, or variational inequalities; the third one causes major difficulties for the system's solvability. Our approach is based on the recent development of the theory on Navier-Stokes variational inequalities.
Numerical weather prediction system: scientific and operational aspects
arXiv (Cornell University), Oct 12, 2018
In this paper we deal with parabolic variational inequalities of Navier-Stokes type with time-dep... more In this paper we deal with parabolic variational inequalities of Navier-Stokes type with time-dependent constraints on velocity fields, including gradient constraint case. One of the objectives of this paper is to propose a weak variational formulation for variational inequalities of Navier-Stokes type and to solve them by applying the compactness theorem, which was recently developed by the authors (cf. [22]). Another objective is to approach to a class of quasi-variational inequalities associated with Stefan/Navier-Stokes problems in which we are taking into account the freezing effect of materials in fluids. As is easily understood, the phase change from liquid into solid gives a great influence to the velocity field in the fluid. For instance, in the mussy region, the velocity of the fluid is constrained by some obstacle caused by moving solid. We shall challenge to the mathematical modeling of Stefan/Navier-Stokes problem as a quasivariational inequality and solve it as an application of parabolic variational inequalities of Navier-Stokes type.
Archives of Medical Science, Dec 8, 2021
The impact of the COVID-19 pandemic on urological care in Poland-Post-COVID resilience scenarios ... more The impact of the COVID-19 pandemic on urological care in Poland-Post-COVID resilience scenarios and recommendations for the healthcare system: A national population-based modelling study Abstract Introduction: Our aim was to assess the time required to recover the hypothetical surgical capacity of urological procedures that were suspended due to lockdowns caused by the SARS-CoV-2 outbreak in 2020 and 2021 in Poland, to indicate the most affected procedures, and to estimate the recovery time after a likely fourth lockdown. Materials and methods: The data aggregates contained the number of patients who underwent specific urological procedures classified in the ICD-9, performed from January 2009 to October 2019, acquired in granulation per month and per single voivodeship, and obtained by healthcare providers such as hospitals, ambulatory units, and primary care facilities. Using the model, we obtained the time required to discharge the excessive load on the healthcare system and the median wait time in the post-lockdown period. We validated the model based on the data aggregates from March to October 2020. Results: Leaving the capacity of the most affected procedures unaltered, or increasing it by 20%, would not reduce the backlog of patients waiting to receive care after the third lockdown. The consequences of a feasible fourth lockdown would cause the necessity of a post-lockdown increase in capacity by more than 50%. P r e p r i n t 2 Conclusion: The availability of the most affected procedures will never achieve the pre-pandemic state without increasing the hypothetical surgical capacity of urological procedures that were suspended due to lockdowns caused by the SARS-CoV-2 outbreak. These procedures require taking special steps to unblock the urological healthcare system and allow patients continuous access to treatment.
Analysis and computations in the four-well problem
Proceedings of the second Polish-Japanese days on : Mathematical aspects of modelling structure formation phenomena
Weak solvability for parabolic variational inclusions and application to quasi-variational problems
Discrete approximation of multiphase Stefan problems with possible degenerations
Current advances in nonlinear analysis and related topics. Collected papers of the conference on nonlinear evolution equations and related topics, Tokyo, Japan, October 10–12, 2009, the 4th Polish-Japanese days on current advances in applied nonlinear analysis and mathematical modelling issues, W...
Stability of a class of nonlinear evolution free boundary problems with respect to domain variations
On some properties of two-phase parabolic free boundary value control problems
Control and cybernetics
Global attractor of a non-isothermal model for phase separation
We consider a non-isothermal model for phase separation dynamics in a binary mixture. The model i... more We consider a non-isothermal model for phase separation dynamics in a binary mixture. The model is described as a system of nonlinear parabolic PDEs which is governed by two physical parameters (absolute temperature and local concentration). The objective of this paper is to construct a global attractor of the semigroup associated with our phase separation model.
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Papers by Marek Niezgódka