时变人口发展方程的解

Solution of a Time-Dependent Population Evolution Equation

通过一适当的变换,时变人口发展方程可表示为如下的抽象发展方程dq/dt=A(1)q+d/dt[G(t)q],q(0)=q_0.本文给出了此方程的唯一解.

By an appropriate transform,the continuous population evolution cquation is expressed as the following abstrac,cvolution equation (dq/dt)=A(t)q+(d/dt)[G(t)q(t)], q(0)=q_0, where A(t)q=-u(r)q(r)-(dq/dr) D(A(t))={q(r)|q(r),A(t)q(r)∈L^2[O,r_m],q(0)=0}. The unique solution of the equation is obtained.