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Approximate controllability of population control system and time-optimal control. (English) Zbl 0696.93010

We study the controllability of a non-stationary population control system of the form \[ \frac{\partial p(r,t)}{\partial t}+\frac{\partial p(r,t)}{\partial r}=-\mu (r,t)p(r,t)+f(r,t),\quad 0<r<r_ m,\quad t>0, \]
\[ p(r,0)=p_ 0(r),\quad 0\leq r\leq r_ m, \]
\[ p(0,t)=\beta (t)\int^{r_ 2}_{r_ 1}k(r,t)h(r,t)p(r,t)dr,\quad t\geq 0, \] The problem of time optimal control is discussed.

MSC:

93B05 Controllability
49J20 Existence theories for optimal control problems involving partial differential equations
92D25 Population dynamics (general)
93C20 Control/observation systems governed by partial differential equations
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