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Find the solution to the following equation for an age-structured population: ∂/∂t P(t,a)+ ∂/∂a P(t,a)=−δ(a)P(t,a), a≥0,t≥0...

Find the solution to the following equation for an age-structured population:
∂/∂t P(t,a)+ ∂/∂a P(t,a)=−δ(a)P(t,a), a≥0,t≥0
P(0,a) = P0(a)
P(t,0) = C
where C > 0 is a constant. Bonus: What is the asymptotic behavior of the population (total size, age-distribution if possible) as t → ∞? If limit exists, is it a solution to the PDE and, if so, what kind of solution?     
Science   Advanced-Physics   
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