scholarly journals Modeling and analysis of adipocytes dynamic with a differentiation process

2020 ◽  
Vol 67 ◽  
pp. 210-241
Author(s):  
Jérôme Gilleron ◽  
Thierry Goudon ◽  
Frédéric Lagoutière ◽  
Hugo Martin ◽  
Benjamin Mauroy ◽  
...  
Keyword(s):  
Experimental Data ◽  
Growth Rate ◽  
Existence And Uniqueness ◽  
Stationary Solutions ◽  
Asymptotic Behavior Of Solutions ◽  
Advection Equation ◽  
Differentiation Process ◽  
Uniqueness Of Solutions ◽  
Modeling And Analysis ◽  
The Mean

We propose in this article a model describing the dynamic of a system of adipocytes, structured by their sizes. This model takes into account the differentiation of a population of mesenchymal cells into preadipocytes and of preadipocytes into adipocytes; the differentiation rates depend on the mean adipocyte radius. The considered equations are therefore ordinary differential equations, coupled with an advection equation, the growth rate of which depends on food availability and on the total surface of adipocytes. Since this velocity is discontinuous, we need to introduce a convenient notion of solutions coming from Filippov theory. We are consequently able to determine the stationary solutions of the system, to prove the existence and uniqueness of solutions and to describe the asymptotic behavior of solutions in some simple cases. Finally, the parameters of the model are fitted thanks to some experimental data and numerical simulations are displayed; a spatial extension of the model is studied numerically.

scholarly journals Asymptotic behavior of non-autonomous fractional p-Laplacian equations driven by additive noise on unbounded domains

2020 ◽  
pp. 2050020
Author(s):  
Renhai Wang ◽  
Bixiang Wang
Keyword(s):  
Asymptotic Behavior ◽  
Existence And Uniqueness ◽  
Additive Noise ◽  
Random Coefficients ◽  
Asymptotic Behavior Of Solutions ◽  
Uniqueness Of Solutions ◽  
Additive White Noise ◽  
Approach Zero ◽  
Drift Terms ◽  
Laplacian Equations

This paper deals with the asymptotic behavior of solutions to non-autonomous, fractional, stochastic [Formula: see text]-Laplacian equations driven by additive white noise and random terms defined on the unbounded domain [Formula: see text]. We first prove the existence and uniqueness of solutions for polynomial drift terms of arbitrary order. We then establish the existence and uniqueness of pullback random attractors for the system in [Formula: see text]. This attractor is further proved to be a bi-spatial [Formula: see text]-attractor for any [Formula: see text], which is compact, measurable in [Formula: see text] and attracts all random subsets of [Formula: see text] with respect to the norm of [Formula: see text]. Finally, we show the robustness of these attractors as the intensity of noise and the random coefficients approach zero. The idea of uniform tail-estimates as well as the method of higher-order estimates on difference of solutions are employed to derive the pullback asymptotic compactness of solutions in [Formula: see text] for [Formula: see text] in order to overcome the non-compactness of Sobolev embeddings on [Formula: see text] and the nonlinearity of the fractional [Formula: see text]-Laplace operator.

scholarly journals A critical statistical study of experimental data on the effect of minute electric currents on the growth rate of the coleoptile of barley

1926 ◽  
Vol 99 (695) ◽  
pp. 122-130 ◽  
Keyword(s):  
Experimental Data ◽  
Growth Rate ◽  
Statistical Study ◽  
Pure Line ◽  
Similar Data ◽  
Electric Currents ◽  
Rate Of Growth ◽  
The Mean ◽  
Positive Results ◽  
Case Based

A study of the effect of very minute electric currents on the rate of growth of the coleoptile of barley was published recently by one of us (F. G. G.) in collaboration. In this paper the mean rate of a number of control coleoptiles was compared with the mean rate of a number exposed to a minute electric discharge. The growth rate of individual coleoptiles showed, naturally, considerable divergences, so the mean result was in each case based on the observation of a large number of coleoptiles, the increments of growth of individual coleoptiles being stated as percentages of the rate of growth during the first hour of observation. It was assumed that the distribution of growth rates in a comparatively large sample of a pure-line barley would conform with the normal distribution; the probable errors of the mean results were therefore calculated in the ordinary way. During the continuation of this work positive results have been obtained in further experimental sets, but a number of these, though significant in the mass, were individually without significance. This suggested that a careful statistical study of the data on which the results were based might show how the accuracy of the method could be increased. Such a study has accordingly been undertaken, and it seems probable that methods employed are likely to be of use in the treatment of similar data.

Stationary solutions of non-autonomous Kolmogorov–Petrovsky–Piskunov equations

1999 ◽  
Vol 19 (3) ◽  
pp. 809-835 ◽  
Author(s):  
V. A. VOLPERT ◽  
YU. M. SUHOV
Keyword(s):  
Existence And Uniqueness ◽  
Space Variable ◽  
Geometric Analysis ◽  
Stationary Solutions ◽  
Classical Approach ◽  
Uniqueness Of Solutions ◽  
New Methods ◽  
Autonomous Equation ◽  
Autonomous Case

The paper is devoted to the following problem: \[ w'' (x) + c w'(x)+ F(w(x),x) = 0, \quad x\in{\mathbb R}^1,\quad w(\pm \infty) = w_{\pm}, \] where the non-linear term $F$ depends on the space variable $x$. A classification of non-linearities is given according to the behaviour of the function $F(w,x)$ in a neighbourhood of the points $w_+$ and $w_-$. The classical approach used in the Kolmogorov–Petrovsky–Piskunov paper [10] for an autonomous equation (where $F=F(u)$ does not explicitly depend on $x$), which is based on the geometric analysis on the $(w,w')$-plane, is extended and new methods are developed to analyse the existence and uniqueness of solutions in the non-autonomous case. In particular, we study the case where the function $F(w,x)$ does not have limits as $x \rightarrow \pm \infty$.

RANDOM ATTRACTORS FOR SECOND ORDER STOCHASTIC LATTICE DYNAMICAL SYSTEMS WITH MULTIPLICATIVE NOISE IN WEIGHTED SPACES

2012 ◽  
Vol 12 (03) ◽  
pp. 1150024 ◽  
Author(s):  
XIAOYING HAN
Keyword(s):  
Existence And Uniqueness ◽  
Multiplicative Noise ◽  
Sufficient Conditions ◽  
Second Order ◽  
Weighted Spaces ◽  
Asymptotic Behavior Of Solutions ◽  
Uniqueness Of Solutions ◽  
Absorbing Sets ◽  
Random Attractors ◽  
Multiplicative White Noise

In this paper, we study the asymptotic behavior of solutions of a second order stochastic lattice differential equation with multiplicative white noise in weighted spaces. We first provide some sufficient conditions for the existence and uniqueness of solutions, and then establish the existence of tempered random bounded absorbing sets and global random attractors.

scholarly journals Asymptotic behavior of solutions for a semibounded nonmonotone evolution equation

2003 ◽  
Vol 2003 (9) ◽  
pp. 521-538
Author(s):  
Nikos Karachalios ◽  
Nikos Stavrakakis ◽  
Pavlos Xanthopoulos
Keyword(s):  
Dynamical System ◽  
Asymptotic Behavior ◽  
Parabolic Equation ◽  
Evolution Equation ◽  
Existence And Uniqueness ◽  
Nonlinear Parabolic Equation ◽  
Evolution Equations ◽  
Asymptotic Behavior Of Solutions ◽  
Uniqueness Of Solutions ◽  
Nonlinear Parabolic

We consider a nonlinear parabolic equation involving nonmonotone diffusion. Existence and uniqueness of solutions are obtained, employing methods for semibounded evolution equations. Also shown is the existence of a global attractor for the corresponding dynamical system.

scholarly journals Asymptotic Behavior of the Solutions of the Generalized Globally Modified Navier–Stokes Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Yonghong Duan ◽  
Xiaojuan Chai
Keyword(s):  
Asymptotic Behavior ◽  
Existence And Uniqueness ◽  
Stokes Equations ◽  
Global Attractors ◽  
Navier Stokes ◽  
Asymptotic Behavior Of Solutions ◽  
Uniqueness Of Solutions ◽  
Navier Stokes Equations

The paper is concerned with the existence and the asymptotic behavior of solutions to a class of generalized Navier–Stokes equations, which generalises the so-called globally modified Navier–Stokes equations. The existence and uniqueness of solutions are proved under different assumptions on the dissipation and modification factors. For the asymptotic behavior of solutions, we prove the existence of global attractors in proper spaces. The results generalize some results derived in our previous work Ann. Polon. Math. 122(2):101–128(2019).

Stationary solutions to a chemotaxis-consumption model with realistic boundary conditions for the oxygen

2019 ◽  
Vol 29 (11) ◽  
pp. 2033-2062 ◽  
Author(s):  
Marcel Braukhoff ◽  
Johannes Lankeit
Keyword(s):  
Boundary Conditions ◽  
Existence And Uniqueness ◽  
Mass Formula ◽  
Stationary Solutions ◽  
Uniqueness Of Solutions ◽  
Flux Boundary Conditions ◽  
Chemotaxis Models ◽  
Consumption Model ◽  
Chemotaxis System ◽  
The Given

Previous studies of chemotaxis models with consumption of the chemoattractant (with or without fluid) have not been successful in explaining pattern formation even in the simplest form of concentration near the boundary, which had been experimentally observed. Following the suggestions that the main reason for that is the usage of inappropriate boundary conditions, in this paper we study the solutions to the stationary chemotaxis system [Formula: see text] in bounded domains [Formula: see text], [Formula: see text], under the no-flux boundary conditions for [Formula: see text] and the physically meaningful condition [Formula: see text] on [Formula: see text], with the given parameter [Formula: see text] and [Formula: see text], [Formula: see text], satisfying [Formula: see text], [Formula: see text] on [Formula: see text]. We prove the existence and uniqueness of solutions for any given mass [Formula: see text]. These solutions are nonconstant.

scholarly journals Predators–prey models with competition, Part I: Existence, bifurcation and qualitative properties

2018 ◽  
Vol 20 (07) ◽  
pp. 1850010 ◽  
Author(s):  
Henri Berestycki ◽  
Alessandro Zilio
Keyword(s):  
Mathematical Model ◽  
Existence And Uniqueness ◽  
Total Population ◽  
Existence Of Solutions ◽  
Asymptotic Properties ◽  
Optimal Solution ◽  
Stationary Solutions ◽  
Qualitative Properties ◽  
Uniqueness Of Solutions ◽  
Strong Competition

We study a mathematical model of environments populated by both preys and predators, with the possibility for predators to actively compete for the territory. For this model we study existence and uniqueness of solutions, and their asymptotic properties in time, showing that the solutions have different behavior depending on the choice of the parameters. We also construct heterogeneous stationary solutions and study the limits of strong competition and abundant resources. We then use these information to study some properties such as the existence of solutions that maximize the total population of predators. We prove that in some regimes the optimal solution for the size of the total population contains two or more groups of competing predators.

The incidence of central serous chorioretinopathy in the population of Kazan: Results of a retrospective epidemiological analysis for 2009–2018

2020 ◽  
pp. 30-33
Author(s):  
D. R. Аgliullin ◽  
G. R. Khasanova ◽  
E. A. Abdulaeva ◽  
S. T. Agliullina ◽  
A. N. Amirov ◽  
...  
Keyword(s):  
Growth Rate ◽  
Central Serous Chorioretinopathy ◽  
Morbidity Rate ◽  
Seasonal Prevalence ◽  
Upward Trend ◽  
Epidemiological Analysis ◽  
Significant Upward Trend ◽  
Track Record ◽  
Minimum Age ◽  
The Mean

Objective: To assess the incidence of central serous chorioretinopathy (CSC) through the example of a large industrial Russian city.Methods: A retrospective analysis of CSC of Kazan population for 2009–2018 has been done.Results: From 2019 to 2018, 831 new cases of CSC were registered in Kazan. A statistically significant upward trend with growth rate 105.2% and accession rate 5.2% was typical for the annual track record. The mean age of patients was 50 years, the minimum age was 14 years, the maximum age was 87 years. A statistically significant upward trend was detected in track record of incidence in groups of 30–39-year-old and 40–49-year-old. Seasonal increase of the incidence was recorded in February, March, April, October, and November.Conclusions: The upward trend and seasonal prevalence are typical for longterm morbidity of CSC in Kazan. The highest morbidity rate of CSC and statistically significant upward trend of its incidence in track record were recorded in the age of 30–39. 

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