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Optimal impulse-control of population dynamics with diffusion. (English) Zbl 0785.92024

Barbu, V. (ed.), Differential equations and control theory. Proceedings of an international conference on differential equations and control theory, held in Iasi, Romania, August 27-September 1, 1990. Harlow: Longman Scientific & Technical. Pitman Res. Notes Math. Ser. 250, 1-6 (1991).
We consider the following population dynamics problem: \[ y_ t+ y_ a+ \mu(a)y- \Delta_ x y= \sum^ n_{i=1} g_ i(a,t)\otimes \delta_{u_ i}\quad\text{in } (0,A)\times \Omega\times (0,T), \]
\[ y(0,x,t)= \int^ A_ 0 b(a)y(a,x,t)da\quad\text{in }\Omega\times (0,T), \]
\[ y(a,x,t)=0 \quad\text{in }(0,A)\times \partial \Omega\times (0,T),\quad y(a,x,0)=y_ 0(a,x)\quad\text{in }(0,A)\times\Omega. \] The control variable represents the spatial position of impulses. The biological significance of such problems is obvious if we view the above system as population dynamics in \(\Omega\), where \(\Omega\) is an open and bounded subset of \(R^ N\) having a sufficiently smooth boundary \(\partial\Omega\).
For the entire collection see [Zbl 0771.00019].

MSC:

92D25 Population dynamics (general)
49J20 Existence theories for optimal control problems involving partial differential equations
49N70 Differential games and control
49N75 Pursuit and evasion games
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