PERSISTENCE OF TRAVELLING WAVEFRONTS IN A GENERALIZED BURGERS-HUXLEY EQUATION WITH LONG-RANGE DIFFUSION

Yanggeng Fu

doi:10.11948/2019.363

2019 Volume 9 Issue 1

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Yanggeng Fu. PERSISTENCE OF TRAVELLING WAVEFRONTS IN A GENERALIZED BURGERS-HUXLEY EQUATION WITH LONG-RANGE DIFFUSION[J]. Journal of Applied Analysis & Computation, 2019, 9(1): 363-372. doi: 10.11948/2019.363

Citation:

Yanggeng Fu. PERSISTENCE OF TRAVELLING WAVEFRONTS IN A GENERALIZED BURGERS-HUXLEY EQUATION WITH LONG-RANGE DIFFUSION[J]. Journal of Applied Analysis & Computation, 2019, 9(1): 363-372. doi: 10.11948/2019.363

PERSISTENCE OF TRAVELLING WAVEFRONTS IN A GENERALIZED BURGERS-HUXLEY EQUATION WITH LONG-RANGE DIFFUSION

Yanggeng Fu

School of Mathematical Sciences, Huaqiao University, Quanzhou, Fujian 362021, China

Author Bio: Email address: fuyanggeng@hqu.edu.cn
Fund Project: The author was supported by National Natural Science Foundation of China (11401229)

Abstract

Abstract

In this paper, we study the persistence of travelling wavefronts in a generalized Burgers-Huxley equation with long-range diffusion. When the influence of long-range diffusion effect is sufficiently small, we prove the persistence of these waves by using geometric singular perturbation theory. When the influence becomes large, the behavior of these waves can only be investigate numerically. In this case, we find that the solutions lose monotonicity by using Matlab program bvp4c. Some previous results are extended.
- Generalized Burgers-Huxley equation /
- travelling wavefronts /
- Fenichel's theory /
- persistence
MSC: 34A34, 34C37, 35B25, 74J35

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References

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