This is a problem about diffusion with population growth.\

^(22)

This is the convolution

c_(0)**f

of

f

with the "Green's function"

c_(0)

for the PDE\ Eduardo D. Sontag, Lecture Notes on Mathematical Systems Biology\ 205\ (a) Show if

c

satisfies (3.1), then, letting

p(x,t):=e^(-\\\\alpha t)c(x,t)

, it follows that

(delp)/(delt)=Dgrad^(2)p

.\ (b) Show directly (plug-in) that (3.3) is a solution of (3.1).

13. This is a problem about diffusion with population growth. 22 This is the convolution c0f of f with the "Green's function" c0 for the PDE iduardo D. Sontag, Lecture Notes on Mathematical Systems Biology 205 (a) Show if c satisfies (3.1), then, letting p(x,t):=etc(x,t), it follows that tp=D2p. (b) Show directly (plug-in) that (3.3) is a solution of (3.1)