Qualitative properties of monostable pulsating fronts: Exponential decay and monotonicity. (English) Zbl 1171.35061
The so-called pulsating front solutions studied in the article under review can be considered as an extension of the classical travelling wave solutions. The author proves the existence and monotonicity (both in space and time) of pulsating front solutions. Moreover, he obtains results about the asymptotic behavior of such solutions, and shows how to use his results to gain deeper understanding about travelling wave solutions.
Reviewer: Sen-Zhong Huang (Hamburg)
MSC:
| 35K55 | Nonlinear parabolic equations |
| 35K57 | Reaction-diffusion equations |
| 35B10 | Periodic solutions to PDEs |
| 35B40 | Asymptotic behavior of solutions to PDEs |
Keywords:
reaction-diffusion equations; periodic solutions; travelling wave solutions; asymptotic behavior of solutionsReferences:
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