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Mathematics 15 Online
OpenStudy (anonymous):

A colony of bacteria is growing on a circular petri dish with radius .05 meters according to the PDE ut = D∆u + 10u. Assume that u = 0 at the boundary of the petri dish. If D is small, then the population of bacteria will grow exponentially forever. If D is large, then the bacteria will eventually die out. How big does D have to be for the bacteria to die out?

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