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Center for Partial Differential Equations, East China Normal University, Minhang, Shanghai 200241, People's Republic of China email: [email protected]
K. NAKASHIMA
Affiliation:
Tokyo University of Marine Science and Technology, 4-5-7 Konan, Minato-ku, Tokyo 108-8477, Japan email: [email protected]
W.-M. NI
Affiliation:
Center for Partial Differential Equations, East China Normal University, Minhang, Shanghai 200241, People's Republic of China email: [email protected]School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA email: [email protected]
This model, proposed by T. Nagylaki, describes the evolution of two alleles under the joint action of selection, migration, and partial panmixia – a non-local term, for the complete dominance case, where g(x) is assumed to change sign at least once to reflect the diversity of the environment. First, properties for general non-local problems are studied. Then, existence of non-trivial steady states, in terms of the diffusion coefficient d and the partial panmixia rate b, is obtained under different signs of the integral ∫Ωg(x)dx. Furthermore, stability and instability properties for non-trivial steady states, as well as the trivial steady states u ≡ 0 and u ≡ 1 are investigated. Our results illustrate how the non-local term – namely, the partial panmixia – helps the migration in this model.
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