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Age-density dependent population dispersal in RN
1University of Connecticut, Storrs 06269-3009, USA. hernande@math.uconn.edu
Abstract:
We discuss an N-dimensional model for diffusion of age dependent populations. Let rho(x, t, a) be the population density at time t, age a and spatial position x, and let u(x, t) = [formula: see text] rho(x, t, a) da be the total population at t and x. The directed dispersal model to be discussed, with diffusion depending on the gradient of the total population, is [formula see text] With some assumptions on the form of the death and birth modulus, this system is reduced to a mixed parabolic-hyperbolic system containing the Porous Medium equation in RN. We discuss the existence, regularity and localization of the solution of this reduced system.
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