Osaka Journal of Mathematics

Entire solutions for a discrete diffusive equation with bistable convolution type nonlinearity

Jong-Shenq Guo and Ying-Chin Lin

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We study entire solutions for a discrete diffusive equation with bistable convolution type nonlinearity. We construct three different types of entire solutions. Each of these entire solutions behaves as two traveling wavefronts connecting two of those three equilibria as time approaches minus infinity. Moreover, the first and second ones are solutions which behave as two traveling wavefronts approaching each other from both sides of $x$-axis. The behavior of the second one is like the first one except it connects two different wavefronts. The third one is a solution which behaves as two different traveling wavefronts and one chases another from the same side of $x$-axis.

Article information

Osaka J. Math., Volume 50, Number 3 (2013), 607-629.

First available in Project Euclid: 27 September 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 34K05: General theory 34A34: Nonlinear equations and systems, general
Secondary: 34K60: Qualitative investigation and simulation of models 34E05: Asymptotic expansions


Guo, Jong-Shenq; Lin, Ying-Chin. Entire solutions for a discrete diffusive equation with bistable convolution type nonlinearity. Osaka J. Math. 50 (2013), no. 3, 607--629.

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