scholarly journals An age-dependent population equation with diffusion and delayed birth process

2005 ◽  
Vol 2005 (20) ◽  
pp. 3273-3289 ◽  
Author(s):  
G. Fragnelli
Keyword(s):  
Asymptotic Behavior ◽  
Semigroup Theory ◽  
New Age ◽  
Well Posedness ◽  
Birth Process ◽  
Age Dependent ◽  
Population Equation

We propose a new age-dependent population equation which takes into account not only a delay in the birth process, but also other events that may take place during the time between conception and birth. Using semigroup theory, we discuss the well posedness and the asymptotic behavior of the solution.

scholarly journals The asymptotic behavior of a population equation with diffusion and delayed birth process

2007 ◽  
Vol 7 (4) ◽  
pp. 735-754 ◽  
Author(s):  
Genni Fragnelli ◽  
◽  
A. Idrissi ◽  
L. Maniar ◽  
◽  
...  
Keyword(s):  
Asymptotic Behavior ◽  
Birth Process ◽  
Population Equation

HOPF BIFURCATION IN AN AGE-DEPENDENT POPULATION MODEL WITH DELAYED BIRTH PROCESS

2012 ◽  
Vol 22 (06) ◽  
pp. 1250146 ◽  
Author(s):  
PING BI ◽  
XIANLONG FU
Keyword(s):  
Steady State ◽  
Hopf Bifurcation ◽  
Population Model ◽  
Semigroup Theory ◽  
Time Lag ◽  
Population System ◽  
Birth Process ◽  
Birth Function ◽  
Age Dependent ◽  
Dynamical Properties

This paper is devoted to the study of an age-dependent population system with Riker type birth function. The time lag factor is considered for the birth process. We investigate some dynamical properties of the equation by using C0-semigroup theory, through which we obtain some conditions of asymptotical stability and Hopf bifurcation occurring at positive steady state for the system.

Well-Posedness of the Gnedenko System with Multiple Vacations

2012 ◽  
Vol 522 ◽  
pp. 902-909
Author(s):  
Bilikiz Yunus ◽  
Abdukerim Haji
Keyword(s):  
Semigroup Theory ◽  
Linear Operators ◽  
Well Posedness ◽  
Multiple Vacations ◽  
Dynamic Solution ◽  
Multiple Vacation ◽  
Gnedenko System

We investigate the solution of the Gnedenko system with multiple vacation of a repairman. By using-semigroup theory of linear operators, we prove well-posedness and the existence of the unique positive dynamic solution of the system.

scholarly journals Asymptotic behavior of supercritical wave equations driven by colored noise on unbounded domains

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Bixiang Wang
Keyword(s):  
Asymptotic Behavior ◽  
Existence And Uniqueness ◽  
Wave Equations ◽  
Colored Noise ◽  
Unbounded Domains ◽  
Strichartz Estimates ◽  
Well Posedness ◽  
Natural Energy ◽  
Random Attractors ◽  
Supercritical Nonlinearity

<p style='text-indent:20px;'>This paper deals with the asymptotic behavior of the non-autonomous random dynamical systems generated by the wave equations with supercritical nonlinearity driven by colored noise defined on <inline-formula><tex-math id="M1">\begin{document}$ \mathbb{R}^n $\end{document}</tex-math></inline-formula> with <inline-formula><tex-math id="M2">\begin{document}$ n\le 6 $\end{document}</tex-math></inline-formula>. Based on the uniform Strichartz estimates, we prove the well-posedness of the equation in the natural energy space and define a continuous cocycle associated with the solution operator. We also establish the existence and uniqueness of tempered random attractors of the equation by showing the uniform smallness of the tails of the solutions outside a bounded domain in order to overcome the non-compactness of Sobolev embeddings on unbounded domains.</p>

scholarly journals Hyperbolic Maxwell variational inequalities of the second kind

2020 ◽  
Vol 26 ◽  
pp. 34 ◽  
Author(s):  
Irwin Yousept
Keyword(s):  
Variational Inequalities ◽  
Existence Result ◽  
Semigroup Theory ◽  
Regularity Property ◽  
Well Posedness ◽  
Test Functions ◽  
Local Boundedness ◽  
Subdifferential Calculus ◽  
Faraday’S Law ◽  
Yosida Regularization

We analyze a class of hyperbolic Maxwell variational inequalities of the second kind. By means of a local boundedness assumption on the subdifferential of the underlying nonlinearity, we prove a well-posedness result, where the main tools for the proof are the semigroup theory for Maxwell’s equations, the Yosida regularization and the subdifferential calculus. The second part of the paper focuses on a more general case omitting the local boundedness assumption. In this case, taking into account more regular initial data and test functions, we are able to prove a weaker existence result through the use of the minimal section operator associated with the Nemytskii operator of the governing subdifferential. Eventually, we transfer the developed well-posedness results to the case involving Faraday’s law, which in particular allows us to improve the regularity property of the electric field in the weak existence result.

Feedback theory to the well-posedness of evolution equations

2020 ◽  
Vol 378 (2185) ◽  
pp. 20190616
Author(s):  
S. Boulite ◽  
S. Hadd ◽  
L. Maniar
Keyword(s):  
Evolution Equations ◽  
Semigroup Theory ◽  
Well Posedness ◽  
Boundary Problems ◽  
Neutral Equations ◽  
Infinite Dimensional ◽  
Research Activities ◽  
Semigroup Approach ◽  
History Of ◽  
And Control

In this paper, we cross the boundary between semigroup theory and general infinite-dimensional systems to bridge the isolated research activities in the two areas. Indeed, we first give a chronological history of the development of the semigroup approach for control theory. Second, we use the feedback theory to prove the well-posedness of a class of dynamic boundary problems. Third, the obtained results are applied to the well-posedness of neutral equations with non-autonomous past. We will also see that the strong connection between semigroup and control theories lies in feedback theory, where different kinds of perturbations appear. This article is part of the theme issue ‘Semigroup applications everywhere’.

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