SEPARATION DICHOTOMY AND WAVEFRONTS FOR A NONLINEAR CONVOLUTION EQUATION

@inproceedings{Gmez2014SEPARATIONDA,
  title={SEPARATION DICHOTOMY AND WAVEFRONTS FOR A NONLINEAR CONVOLUTION EQUATION},
  author={Carlos G{\'o}mez and Humberto Prado and Sergei I. Trofimchuk},
  year={2014}
}
This paper is concerned with a scalar nonlinear convolution equation which appears naturally in the theory of traveling waves for monostable evolution models. First, we prove that each bounded positive solution of the convolution equation should either be asymptotically separated from zero or it should converge (exponentially) to zero. This dichotomy principle is then used to establish a general theorem guaranteeing the uniform persistence and existence of semi-wavefront solutions to the… CONTINUE READING

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Asymptotic Behavior, Spreading Speeds, and Traveling Waves of Nonmonotone Dynamical Systems

  • SIAM J. Math. Analysis
  • 2015
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