Entire solution in an ignition nonlocal dispersal equation: Asymmetric kernel View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2017-10

AUTHORS

Li Zhang, WanTong Li, ZhiCheng Wang

ABSTRACT

This paper mainly focuses on the front-like entire solution of a classical nonlocal dispersal equation with ignition nonlinearity. Especially, the dispersal kernel function J may not be symmetric here. The asymmetry of J has a great influence on the profile of the traveling waves and the sign of the wave speeds, which further makes the properties of the entire solution more diverse. We first investigate the asymptotic behavior of the traveling wave solutions since it plays an essential role in obtaining the front-like entire solution. Due to the impact of f′(0) = 0, we can no longer use the common method which mainly depends on Ikehara theorem and bilateral Laplace transform to study the asymptotic rates of the nondecreasing traveling wave and the nonincreasing one tending to 0, respectively, so we adopt another method to investigate them. Afterwards, we establish a new entire solution and obtain its qualitative properties by constructing proper supersolution and subsolution and by classifying the sign and size of the wave speeds. More... »

PAGES

1791-1804

References to SciGraph publications

  • 2009-05. Travelling wave fronts in nonlocal delayed reaction-diffusion systems and applications in ZEITSCHRIFT FÜR ANGEWANDTE MATHEMATIK UND PHYSIK
  • 2016-03. Multi-type Entire Solutions in a Nonlocal Dispersal Epidemic Model in JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS
  • 2006-10. Entire Solutions with Merging Fronts to Reaction–Diffusion Equations in JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS
  • 2016-10. Existence, uniqueness and stability of pyramidal traveling fronts in reaction-diffusion systems in SCIENCE CHINA MATHEMATICS
  • Journal

    TITLE

    Science China Mathematics

    ISSUE

    10

    VOLUME

    60

    Author Affiliations

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s11425-016-9003-7

    DOI

    http://dx.doi.org/10.1007/s11425-016-9003-7

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1085425286


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