Using NIntegrate/Integrate as boundary condition inside NDSolve

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I try to implement a population model with age structure in Mma12 using NDSolve to get a numerical solution for my PDE. However, one boundary condition involves an integral, which gives me problems (using either Integrate or NIntegrate).

NDSolve[{D[n[t, a], t] + D[n[t, a], a] == -0.00002*Exp[0.099*t]*
n[t, a],n[0, a] == 100*Exp[-0.0163*(a - 30.8)^2], n[t, 0] == Integrate[
0.1134*Exp[-0.0163*(a - 30.8)^2]*n[t, a2], {a2, 0, 100}]}, n[t, a], {t, 0, 100}, {a, 0, 100}]

In this post they used a trick to avoid the integral, but I don’t think I can use it in my case. Any help is appreciated.