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Global boundedness of the solutions to a Gurtin-MacCamy system |
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| Authors: | M Iannelli M-Y Kim E-J Park A Pugliese |
| Institution: | (1) Dipartimento di matematica, Università di Trento, Italy, e-mail: 1iannelli@science.unitn.it, IT;(2) Department of Mathematics, Inha University, Inchon 402-751, Korea, e-mail:mykim@math.inha.ac.kr, IT;(3) Department of Mathematics, Yonsei University, Seoul 120-749, Korea, e-mail: ejpark@math.yonsei.ac.kr , KR;(4) Dipartimento di Matematica, Università di Trento, Italy, e-mail: pugliese@science.unitn.it, IT |
| Abstract: | This paper is concerned with the analysis of a generalized Gurtin-MacCamy model describing the evolution of an age-structured population. The problem of global boundedness is studied. Namely we ask whether there are simple general assumptions that one can make on the vital rates in order to have boundedness of the solution. Next a fully implicit finite difference scheme along the characteristic is considered to approximate the solution of the system. Global boundedness of the numerical solutions is investigated. The optimal rate of convergence of the scheme is obtained in the maximum norm. Numerical examples are presented. |
| Keywords: | and phrases: Population dynamics age-structure finite difference method of characteristics asymptotic behavior |
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