Spreading speeds and traveling waves for nonlocal dispersal equations with degenerate monostable nonlinearity

By Guo‐Bao Zhang, Wan-Tong Li, Zhi-Cheng Wang. 2012

123 citations recorded by the source corpus.

Abstract This paper is concerned with the spreading speeds and traveling wave solutions of a nonlocal dispersal equation with degenerate monostable nonlinearity. We first prove that the traveling wave solution ϕ ( ξ ) with critical minimal speed c = c ⁎ decays exponentially as ξ → − ∞ , while other traveling wave solutions ϕ ( ξ ) with c > c ⁎ do not decay exponentially as ξ → − ∞ . Then the monotonicity and uniqueness (up to translation) of traveling wave solution with critical minimal speed is established. Finally, we prove that the critical minimal wave speed c ⁎ coincides with the asymptotic speed of spread.

Subfields: Applied Mathematics, Modeling and Simulation, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/ba2b095211ac927c3b124e5fc2adbdacc324fc7c

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In Applied Mathematics

In Modeling and Simulation

In Public Health, Environmental and Occupational Health

Citations in the corpus

Approximations of random dispersal operators/equations by nonlocal dispersal operators/equations (2014, background): “dy +F(t,x,u), x ∈ D,¯ Bn,bu(t,x) = 0, x ∈ Db if Db 6= ∅, (1.2) are often used to model diﬀusive systems which exhibit nonlocal internal interactions and have been recently studied by many people (see [4, 7, 8, 9, 12, 13, 14, 18, 21, 26, 28, 30, 31, 44], etc.). In (1.2), D is either a smooth bounded ”