Abstract.
We establish the existence of traveling wave solutions for a nonlinear partial differential equation that models a logistically growing population whose movement is governed by an advective process. Conditions are presented for which traveling wave solutions exist and for which they are stable to small semi-finite domain perturbations. The wave is of mathematical interest because its behavior is determined by a singular differential equation and those with small speed of propagation steepen into a shock-like solutions. Finally, we indicate that the smoothing presence of diffusion allows wave persistence when an advective slow moving wave may collapse.
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Received: 24 November 1997 / Revised version: 13 July 1998
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Lika, K., Hallam, T. Traveling wave solutions of a nonlinear reaction–advection equation. J Math Biol 38, 346–358 (1999). https://doi.org/10.1007/s002850050152
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DOI: https://doi.org/10.1007/s002850050152