On a model of a population with variable motility
Olga Turanova
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Source: Crossref
Published: Jun 22, 2015
DOI: 10.1142/s0218202515500505
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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.
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