Stability on solution of population evolution equations with applications (Q2764909)

This paper deals with the study of the non-stationary population evolution equation NEWLINE\[NEWLINE\begin{cases} {\partial P\over\partial r}+{\partial P\over\partial t}+B(r,t)P=A(r,t)P+ G(r,t),\\ P(r,0)=P_0(r),\\ P^T(0,t)=V(t)= \bigl(v_1(t), \dots, v_n(t) \bigr),\\ v_i(t)=p_i(t)\int^{r_{i_2}}_{r_{i_1}} h_i(r,t) k_i(r,t) P_i(r,t)dr. \end{cases}NEWLINE\]NEWLINE The authors prove that this non-homogeneous boundary value problem is well posed in Sobolev space \(H^{3/2,3/2}(\Omega)\). This result provides a strictly mathematical basis for further research of population control problems.