Give an explicit representation for the solution of this population model. parti

Question

Give an explicit representation for the solution of this population model. partial derivative u/partial derivative t = 3u + 2 partial derivative^2 u/partial derivative x^2 for all x on the real line and t > 0. u(x, 0) = x(1 - x) on 0 lessthanorequalto x lessthanorequalto 1 and 0 elsewhere. One can assume the heat kernel representation for the heat equation on the real line. The integration in the representation does not need to be completed. What is the speed of propagation in this problem? Why?

Explanation / Answer

b)Speed of propagation is infinite. This is because initial condition has support, that is contained within some compact region.

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