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Volume 39, Issue 1
Traveling Waves in Degenerate Diffusion Equations

Tianyuan Xu & Jingxue Yin

DOI: 10.4208/cmr.2021-0102

Commun. Math. Res., 39 (2023), pp. 36-53.

Published online: 2022-10

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  • Abstract

In this survey, we present a literature review on the study of traveling waves in degenerate diffusion equations by illustrating the interesting and singular wave behavior caused by degeneracy. The main results on wave existence and stability are presented for the typical degenerate equations, including porous medium equations, flux limited diffusion equations, delayed degenerate diffusion equations, and other strong degenerate diffusion equations.

  • Keywords

Traveling waves, degenerate diffusion equation, existence, stability.

  • AMS Subject Headings

35K65, 35K57, 35C07, 35B40, 92D25

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-39-36, author = {Xu , Tianyuan and Yin , Jingxue}, title = {Traveling Waves in Degenerate Diffusion Equations}, journal = {Communications in Mathematical Research }, year = {2022}, volume = {39}, number = {1}, pages = {36--53}, abstract = {

In this survey, we present a literature review on the study of traveling waves in degenerate diffusion equations by illustrating the interesting and singular wave behavior caused by degeneracy. The main results on wave existence and stability are presented for the typical degenerate equations, including porous medium equations, flux limited diffusion equations, delayed degenerate diffusion equations, and other strong degenerate diffusion equations.

}, issn = {2707-8523}, doi = {https://doi.org/10.4208/cmr.2021-0102}, url = {http://global-sci.org/intro/article_detail/cmr/21077.html} }
TY - JOUR T1 - Traveling Waves in Degenerate Diffusion Equations AU - Xu , Tianyuan AU - Yin , Jingxue JO - Communications in Mathematical Research VL - 1 SP - 36 EP - 53 PY - 2022 DA - 2022/10 SN - 39 DO - http://doi.org/10.4208/cmr.2021-0102 UR - https://global-sci.org/intro/article_detail/cmr/21077.html KW - Traveling waves, degenerate diffusion equation, existence, stability. AB -

In this survey, we present a literature review on the study of traveling waves in degenerate diffusion equations by illustrating the interesting and singular wave behavior caused by degeneracy. The main results on wave existence and stability are presented for the typical degenerate equations, including porous medium equations, flux limited diffusion equations, delayed degenerate diffusion equations, and other strong degenerate diffusion equations.

Tianyuan Xu & Jingxue Yin. (2022). Traveling Waves in Degenerate Diffusion Equations. Communications in Mathematical Research . 39 (1). 36-53. doi:10.4208/cmr.2021-0102
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