Olga Turanova
Published 2014-09-16Version 1
We study a reaction-diffusion equation with a nonlocal reaction term that models a population with variable motility. We establish a global supremum bound for solutions of the equation. We investigate the asymptotic (long-time and long-range) behavior of the population. We perform a certain rescaling and prove that solutions of the rescaled problem converge locally uniformly to zero in a certain region and stay positive (in some sense) in another region. These regions are determined by two viscosity solutions of a related Hamilton-Jacobi equation.
Keller-Segel model with Logarithmic Interaction and nonlocal reaction term
A Hamilton-Jacobi approach for a model of population structured by space and trait
Invasion fronts with variable motility: phenotype selection, spatial sorting and wave acceleration
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