By Sebastian Aniţa (auth.)

ISBN-10: 9048155908

ISBN-13: 9789048155903

ISBN-10: 9401594368

ISBN-13: 9789401594363

The fabric of the current ebook is an extension of a graduate direction given by means of the writer on the collage "Al.I. Cuza" Iasi and is meant for stu dents and researchers attracted to the functions of optimum keep an eye on and in mathematical biology. Age is likely one of the most vital parameters within the evolution of a bi ological inhabitants. whether for a truly lengthy interval age constitution has been thought of simply in demography, these days it truly is primary in epidemiology and ecology too. this is often the 1st e-book dedicated to the regulate of constant age dependent populationdynamics.It specializes in the elemental houses ofthe options and at the regulate of age established inhabitants dynamics without or with diffusion. the most objective of this paintings is to familiarize the reader with crucial difficulties, methods and leads to the mathematical thought of age-dependent versions. specific consciousness is given to optimum harvesting and to precise controllability difficulties, that are vitally important from the econom ical or ecological issues of view. We use a few new techniques and strategies in smooth keep watch over thought resembling Clarke's generalized gradient, Ekeland's variational precept, and Carleman estimates. The equipment and strategies we use may be utilized to different keep watch over problems.

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The cloth of the current ebook is an extension of a graduate direction given by way of the writer on the college "Al. I. Cuza" Iasi and is meant for stu dents and researchers attracted to the purposes of optimum regulate and in mathematical biology. Age is without doubt one of the most vital parameters within the evolution of a bi ological inhabitants.

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

**Sample text**

It is obvious that a* < 0 00 if and only if £(K)(O) = K(s)ds < 1. 6) . Then and since £(K)' (o") 1 00 = e-uotcos(vat)K(t)dt < 1 00 e-uotK(t)dt and as a consequence we get that ua = Ra < o" . 2. The solution b of (3. 7) O. ~ Proof. R'x>0 £(K)(>') = lim I,X I..... 8) (see [34]) we conclude that lim 1,X1..... R>' > 0 £(F)(>' )£(K)(>') = O. :. :iY:.. :. :. :)(:.. 9) ANALYSIS OF AGE-DEPENDENT POPULATION DYNAMICS where x E R 'is such that £(K)(x + i y) implies that m(x) = inf 11 yeR - =1= 45 1, Vy E R.

Proof. R'x>0 £(K)(>') = lim I,X I..... 8) (see [34]) we conclude that lim 1,X1..... R>' > 0 £(F)(>' )£(K)(>') = O. :. :iY:.. :. :. :)(:.. 9) ANALYSIS OF AGE-DEPENDENT POPULATION DYNAMICS where x E R 'is such that £(K)(x + i y) implies that m(x) = inf 11 yeR - =1= 45 1, Vy E R. 8) £(K)(x + iy) 1> 0. Define the functions e-xtF (t), Ix (t) = { 0, and t ~ 0, t < 0, e-xtK(t) , t~O , kx (t) = { t < 0. 0, Since Ix and k x vanish outside of [0, at], their Fourier transforms lx, k x belong to L 2(R) and we can also verify that lx(y) = £(F)(x Thus i: I and so + iy) , kx(Y) = £(K)(x + iy).

Sign w(a, t + a)da, tER .

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

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