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1
Content available remote Unconditionally positive NSFD and classical finite difference schemes for biofilm formation on medical implant using Allen-Cahn equation
Tijani Yusuf O., Appadu Appanah Rao
Demonstratio Mathematica
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2022
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Vol. 55, nr 1
40--60
EN
The study of biofilm formation is becoming increasingly important. Microbes that produce biofilms have complicated impact on medical implants. In this paper, we construct an unconditionally positive non-standard finite difference scheme for a mathematical model of biofilm formation on a medical implant. The unknowns in many applications reflect values that cannot be negative, such as chemical component concentrations or population numbers. The model employed here uses the bistable Allen-Cahn partial differential equation, which is a generalization of Fisher’s equation. We study consistency and convergence of the scheme constructed. We compare the performance of our scheme with a classical finite difference scheme using four numerical experiments. The technique used in the construction of unconditionally positive method in this study can be applied to other areas of mathematical biology and sciences. The results here elaborate the benefits of the non-standard approximations over the classical approximations in practical applications.
2
Content available remote Existence and uniqueness of the weak solution for Keller-Segel model coupled with Boussinesq equations
Slimani Ali, Bouzettouta Lamine, Guesmia Amar
Demonstratio Mathematica
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2021
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Vol. 54, nr 1
558--575
EN
Keller-Segel chemotaxis model is described by a system of nonlinear partial differential equations: a convection diffusion equation for the cell density coupled with a reaction-diffusion equation for chemoattractant concentration. In this work, we study the phenomenon of Keller-Segel model coupled with Boussinesq equations. The main objective of this work is to study the global existence and uniqueness and boundedness of the weak solution for the problem, which is carried out by the Galerkin method.
3
Content available remote Complete convergence under special hypotheses
Stoica G.
Journal of Mathematics and Applications
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2012
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Vol. 35
91-95
EN
We prove Baum-Katz type theorems along subsequences of random variables under Komlós-Saks and Mazur-Orlicz type boundedness hypotheses.
4
Content available remote Patterns of boundedness of the rational system xn+1 = ...[wzór] and yn+1 = ...[wzór]
Camouzis E., Drymonis E., Ladas G.
Fasciculi Mathematici
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2010
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Nr 44
9-18
EN
We establish the boundedness character of solutions of the rational system in the title, with the parameters α1, β1 positive and the remaining eight parameters nonnegative and with arbitrary nonnegative initial conditions such that the denominators are always positive. We present easily verifiable necessary and sufficient conditions, explicitly stated in terms of the parameters, which determine the boundedness character of the system.
5
Content available remote On the solutions of a rational system of difference equations
Elsayed E. M.
Fasciculi Mathematici
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2010
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Nr 45
25-36
EN
In this paper we deal with the solutions of the system of the difference equations xn+1 = ...[wzór], yn+1 = ...[wzór], with a nonzero real numbers initial conditions.
6
Content available remote On the difference equation xn+1 = α + ...[wzór]
Yalçinkaya ĺ.
Fasciculi Mathematici
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2009
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Nr 42
133-139
EN
In this paper, we investigate the global behavior of the difference equation of order three xn+1 = α + ...[wzór], n = 0, 1,… where the parameters α, k ∈ (0, ∞) and the initial values x-2, x-1 and x0 are arbitrary positive real numbers.
7
Content available remote On some fundamental aspects of certain sum-difference equations
Pachpatte B. G.
Fasciculi Mathematici
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2009
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Nr 41
119-134
8
Content available remote Sequences which satisfy a logarithmic linear inequality
Stević S.
Fasciculi Mathematici
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2004
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Nr 34
85-95
EN
In this note we discuss the boundedness and convergence of a sequence which satisfies the following logarithmic linear inequality where k(1) + k(2) +... + km = 1. We focus our attention especially to the case n = 2. Also we describe a situation where this inequality occurs naturally.
9
Content available remote Stability for certain fourth order nonlinear differential equations
Lin S., Liu Z., Yu Y.
Demonstratio Mathematica
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1998
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Vol. 31, nr 1
87-96
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