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ASYMPTOTIC ANALYSIS OF A MONOSTABLE EQUATION IN PERIODIC MEDIA
並列摘要
We consider a multidimensional monostable reaction-diffusion equation whose nonlinearity involves periodic heterogeneity. This serves as a model of invasion for a population facing spatial heterogeneities. As a rescaling parameter tends to zero, we prove the convergence to a limit interface, whose motion is governed by the minimal speed (in each direction) of the underlying pulsating fronts. This dependance of the speed on the (moving) normal direction is in contrast with the homogeneous case and makes the analysis quite involved. Key ingredients are the recent improvement [4] of the well-known spreading properties [32], [9], and the solution of a Hamilton-Jacobi equation.
並列關鍵字
無資料被引用紀錄
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延伸閱讀
- Chang, C. H. (2011). Asymptotic Theory for Geostatistical Model Selection [doctoral dissertation, National Chiao Tung University]. Airiti Library. https://doi.org/10.6842/NCTU.2011.00116
- Chi, C. M. (2020). Asymptotic Analysis of Prediction Error for Linear and NonlinearTime Series [doctoral dissertation, National Taiwan University]. Airiti Library. https://doi.org/10.6342/NTU202000243
- Zhang, G. L., Song, M. H., & Liu, M. Z. (2012). Asymptotic Stability of a Class of Impulsive Delay Differential Equations. Journal of Applied Mathematics, 2012(), 1492-1500-598. https://doi.org/10.1155/2012/723893
- Gumus, M., & Ocalan, O. (2014). Global Asymptotic Stability of a Nonautonomous Difference Equation. Journal of Applied Mathematics, 2014(), 318-322-336. https://doi.org/10.1155/2014/395954
- Han, M. A., Yu, P., Romanovski, V. G., & Zhang, T. H. (2014). Periodic Solutions and Asymptotic Analysis of Ordinary Differential Equations. Abstract and Applied Analysis, 2014(), 614-614-368. https://doi.org/10.1155/2014/291482