Math 5120, Homework 7.1, due March 2

Math 5120, Homework 7.1, due March 2
1. Write a two-dimensional version of the model for the cellular slime mold
interaction with cAMP (equations and boundary conditions) Write a linearized
version for perturbatoins from the homogeneous solution.
2. Which of the following procedures would tend to promote the onset of
agregation? Explain.
a) placing barriers so that the domain is sundivided into several subregionso
b) increasing the amount of cAMP concentration in the initial homogeneous
c) raising the temperature
d) adding to the medium phosphodiesterase, an enzyme that degrades cAMP
3. Assume in the aggregation model that L = 1, D = .1, k = .1, µ = .01,
χ = 2, ā=1, f = .05. What is the value of c̄? What is the maximum value
of n that will support the aggregation? Plot a(x, t) = ā + ã as a function of x
for several values of time to observe aggregation. Repeat this plot for different
values of n.
(extra credit) generalize the solution for perturbations from homogeneous
state to two dimensions. Plot as a series of color-coded 2d plots (one for each
time point) or as a movie.