Analysis And Control Of Age-Dependent Population Dynamics Book

	Preface	vii
	Notations	ix
1	Introduction	1
1.1	Overview of the problems	1
1.2	General models of population dynamics with diffusion	6
1.3	Age-dependent epidemic models	10
2	Analysis of Age-Dependent Population Dynamics	15
2.1	The linear age-dependent model	15
2.2	A general nonlinear model	29
2.3	Asymptotic behaviour of the solution	42
2.4	A linear periodic age-dependent population dynamics	51
2.5	Exercises	60
3	Optimal Control of Population Dynamics	65
3.1	Optimal harvesting for linear age-dependent population dynamics	67
3.2	Optimal harvesting for a nonlinear model	75
3.3	Optimal harvesting for a linear periodic population dynamics	88
3.4	A nonlinear optimal control problem	95
3.5	Exercises	104
4	Analysis of Population Dynamics with Diffusion	109
4.1	Basic properties of the solution. The linear model	109
4.2	A general nonlinear model	123
4.3	Asymptotic behaviour of the solution	128
4.4	Exercises	132
5	Control of Population Dynamics with Diffusion	137
5.1	Optimal harvesting for a general nonlinear model	137
5.2	A null controllability problem with distributed parameter	147
5.3	A local exact controllability result	154
5.4	Exercises	167
Appendix 1	Elements of Nonlinear Analysis	171
A1.1	Convex functions and subdifferentials	171
A1.2	Generalized gradients of locally Lipschitz functions	177
A1.3	The Ekeland variational principle	180
Appendix 2	The Linear Heat Equation	183
	References	193
	Index	199