Abstract
In this paper we will establish nonlinear a priori lower and upper bounds for the solutions to a large class of equations which arise from the study of traveling wave solutions of reaction–diffusion equations, and we will apply our nonlinear bounds to the Lotka–Volterra system of two and four competing species as examples. The idea used in a series of papers by the first author et al. for the establishment of the linear N-barrier maximum principle will also be used in the proof.
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Acknowledgements
The authors are grateful to the anonymous referees for many helpful comments and valuable suggestions on this paper. L.-C. Hung thanks for the hospitality he received from Karlsruhe Institute of Technology while visiting KIT. L.-C. Hung’s work is partially supported by the Ministry of Science and Technology of Taiwan via the grant MOST 108-2115-M-002-013-MY3.
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Hung, LC., Liao, X. Nonlinear estimates for traveling wave solutions of reaction diffusion equations. Japan J. Indust. Appl. Math. 37, 819–830 (2020). https://doi.org/10.1007/s13160-020-00420-4
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DOI: https://doi.org/10.1007/s13160-020-00420-4