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Asymptotic spreading of interacting species with multiple fronts I: A geometric optics approach
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We establish spreading properties of the Lotka-Volterra competition-diffusion system. When the initial data vanish on a right half-line, we derive the exact spreading speeds and prove the convergence to homogeneous equilibrium states between successive invasion fronts. Our method is inspired by the geometric optics approach for Fisher-KPP equation due to Freidlin, Evans and Souganidis. Our main result settles an open question raised by Shigesada et al. in 1997, and shows that one of the species spreads to the right with a nonlocally pulled front.
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Cited by 1 Pith paper
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On the logarithmic correction of transition fronts in shifting environments
For Fisher-KPP equations with a piecewise-constant shifting environment, the paper derives the exact logarithmic correction to the front location, extending Bramson's correction to growing domains and moving habitat b...
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