Traveling waves in nonclassical diffusion equations
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915576902844416 |
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| author | Barker, William Dong, Le Xuan Luong, Vu Trong Toan, Nguyen Duong |
| author_facet | Barker, William Dong, Le Xuan Luong, Vu Trong Toan, Nguyen Duong |
| contents | We study the existence of monotone traveling wave solutions in a class of nonclassical diffusion equations that include both standard diffusion and a higher-order mixed space-time dispersive term. The reaction term is nonlinear and subject to general structural conditions. By employing the method of upper and lower solutions, using less smooth super and subsolutions, we construct a monotone iterative scheme within a convex set and prove its convergence using Schauder's fixed point theorem. Explicit constructions of super and subsolutions are provided. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_22349 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Traveling waves in nonclassical diffusion equations Barker, William Dong, Le Xuan Luong, Vu Trong Toan, Nguyen Duong Analysis of PDEs 35C07, 35K57 We study the existence of monotone traveling wave solutions in a class of nonclassical diffusion equations that include both standard diffusion and a higher-order mixed space-time dispersive term. The reaction term is nonlinear and subject to general structural conditions. By employing the method of upper and lower solutions, using less smooth super and subsolutions, we construct a monotone iterative scheme within a convex set and prove its convergence using Schauder's fixed point theorem. Explicit constructions of super and subsolutions are provided. |
| title | Traveling waves in nonclassical diffusion equations |
| topic | Analysis of PDEs 35C07, 35K57 |
| url | https://arxiv.org/abs/2510.22349 |