Analysis and Control of Age-Dependent Population Dynamics by Sebastian Aniţa (auth.)

By Sebastian Aniţa (auth.)

The fabric of the current publication is an extension of a graduate direction given through the writer on the collage "Al.I. Cuza" Iasi and is meant for stu­ dents and researchers drawn to the functions of optimum keep watch over and in mathematical biology. Age is likely one of the most vital parameters within the evolution of a bi­ ological inhabitants. no matter if for a truly lengthy interval age constitution has been thought of in simple terms in demography, these days it really is primary in epidemiology and ecology too. this can be the 1st ebook dedicated to the keep an eye on of continuing age based populationdynamics.It specializes in the fundamental houses ofthe ideas and at the keep an eye on of age established inhabitants dynamics without or with diffusion. the most aim of this paintings is to familiarize the reader with crucial difficulties, techniques and leads to the mathematical thought of age-dependent versions. specified cognizance is given to optimum harvesting and to distinct controllability difficulties, that are vitally important from the econom­ ical or ecological issues of view. We use a few new thoughts and strategies in sleek keep an eye on idea comparable to Clarke's generalized gradient, Ekeland's variational precept, and Carleman estimates. The tools and strategies we use should be utilized to different regulate problems.

Show description

Read or Download Analysis and Control of Age-Dependent Population Dynamics PDF

Best calculus books

Integral equations and applications

The aim of this booklet is threefold: for use for graduate classes on quintessential equations; to be a reference for researchers; and to explain equipment of software of the speculation. the writer emphasizes the position of Volterra equations as a unifying software within the research of sensible equations, and investigates the relation among summary Volterra equations and different forms of functional-differential equations.

Matrix Differential Calculus With Applications in Statistics and Econometrics, Third Edition (Wiley Series in Probability and Statistics)

This article is a self-contained and unified therapy of matrix differential calculus, particularly written for econometricians and statisticians. it will probably function a textbook for complex undergraduates and postgraduates in econometrics and as a reference ebook for practicing econometricians.

Stochastic Processes and Operator Calculus on Quantum Groups

This publication goals to give numerous new advancements on stochastic tactics and operator calculus on quantum teams. issues that are handled comprise operator calculus, twin representations, stochastic approaches and diffusions, Appell polynomials and platforms in reference to evolution equations. viewers: This quantity comprises introductory fabric for graduate scholars who're new to the sphere, in addition to extra complex fabric for experts in chance conception, algebraic buildings, illustration thought, mathematical physics and theoretical physics.

Extra info for Analysis and Control of Age-Dependent Population Dynamics

Sample text

E. e. min{T, at} l at (3(a, t) < t < T. I(3l1 u xl(QT ) . lIn - IIILI(QT) ' which implies that Fn -+ F in LOO(O ,T) as n -+ +00. 7) we may infer via Bellman's lemma that bIn -+ b in Loo(O , T) . 7) correspo nding to F := Fn (and consequently to I := In) . 4) it follows that Pn -+ pin Loo(O,TjL1(O,at» and thus (iii) is proved. 3. e. e. 1) . These show that the biological meaning of at is the maximal age of the population. 13) is satisfied then (A4) holds. So, (A4) is the necessary and sufficient condition to have at as the maximal age of the population species.

F)()")£(K)()") 9 1 - £(K)()") (this follows by a classical result from Laplace transform theory; see [34]) . ,) = F(t) + g(t) , t E R+. 46 CHAPTER 2 So, the asymptotic behaviour of b is given by the asymptotic behaviour of g. RA < Xl . 10), from X to X l. tdAI l XI-i oo e- (o" - xJlt m (xd ° 1 - £(K)(A) IlfxIIL(R) · l k t 2(R). ~ ~ x I It is obvious that u = if and only if F (t) = 0, "It ~ 0. 7) is satisfied. 7). 1. e. aE (O,at), ° we where ,6 is extended by 0 outside [0, at]· This happens if the support of,6 lies to the left of the support of Po (po is called in this case a trivial datum) .

E, in (0, T) . e. in QT. 4 - continued. 23) cp(at> t) = 0 t E (O,T). 23) belongs to

Download PDF sample

Rated 4.84 of 5 – based on 34 votes