Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

Localization of age-dependent anti-crowding populations


Author: Gastón E. Hernández
Journal: Quart. Appl. Math. 53 (1995), 35-52
MSC: Primary 92D25; Secondary 35Q80
DOI: https://doi.org/10.1090/qam/1315446
MathSciNet review: MR1315446
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Abstract | References | Similar Articles | Additional Information

Abstract: In this work we prove the existence of solutions and study the localization and nonlocalization of the population in the Gurtin-MacCamy model with age-dependence and diffusion

$\displaystyle \frac{{\partial \rho }}{{\partial t}} + \frac{{\partial \rho }}{{\partial a}} = {(\rho {u_x})_x} - \mu (a, u)\rho $

,

$\displaystyle \rho (x, t, 0) = \int_0^\infty {\beta (a, u)\rho (x, t, a) da}$

,

$\displaystyle \rho (x, 0, a) = {\rho _0}(x, a) \ge 0$

, where

$\displaystyle u(x, t) = \int_0^\infty {\rho (x, t, a) da}$

and

$\displaystyle \beta (a, u) = \beta (u)\sum\limits_{k = 1}^n {{b_k}{a^k}{e^{ - \alpha a}}, \qquad \mu (a, u) = \mu (u)}$

.

References [Enhancements On Off] (What's this?)

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DOI: https://doi.org/10.1090/qam/1315446
Article copyright: © Copyright 1995 American Mathematical Society

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