Some generalizations coming from the study of the discrete nagumo equation

Abstract:

The discrete Nagumo equation corresponds to: 𝑢̇𝑛= 𝑑 (𝑢𝑛− 1− 2𝑢𝑛+ 𝑢𝑛+ 1)+ 𝑓 (𝑢𝑛), 𝑛∈ ℤ and in this work we obtain results concerning the following generalization: 𝑢̇𝑛= 𝑑 (𝑎𝑢𝑛− 1+ 𝑏𝑢𝑛+ 𝑐𝑢𝑛+ 1)+ 𝑓 (𝑢𝑛), 𝑛∈ ℤ With a, b and c being parameters such that a+ b+ c= 0 with a≥ c≥ 0. We have obtained results that generalize part of the work developed by Bertram Zinner [1] and these constitute a starting point for later obtaining what would be the existence of solutions of the traveling wave type in the equation that we consider.

Año de publicación:

2021

Keywords:

Fuente:

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