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Asymptotic spreading of interacting species with multiple fronts. I: A geometric optics approach. (English) Zbl 1439.35286

Summary: 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 N. Shigesada and K. Kawasaki [Biological Invasions: theory and practice. Oxford: Oxford University Press (1997)], and shows that one of the species spreads to the right with a nonlocally pulled front.

MSC:

35K58 Semilinear parabolic equations
35B40 Asymptotic behavior of solutions to PDEs
35D40 Viscosity solutions to PDEs
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