Analytical and numerical investigation of traveling waves for the Allen-Cahn model with relaxation
Overview & Synopsis
A modification of the parabolic Allen-Cahn equation, determined by the substitution of Fick's diffusion law with a relaxation relation of Cattaneo-Maxwell type, is considered. The analysis concentrates on traveling fronts connecting the two stable states of the model, investigating both the aspects of existence and stability. The main contribution is the proof of the nonlinear stability of the wave, as a consequence of detailed spectral and linearized analyses. In addition, numerical studies are performed in order to determine the propagation speed, to compare it to the speed for the parabolic case, and to explore the dynamics of large perturbations of the front.
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Document Information
| Document Title | Analytical and numerical investigation of traveling waves for the Allen-Cahn model with relaxation |
|---|---|
| Author / Organization | Corrado Lattanzio, Corrado Mascia, Ramon G. Plaza, Chiara Simeoni |
| Subject & Discipline | Multidisciplinary Academic Open Research |
| Categories | Science & Mathematics |
| Publication Year | 2014 |
| License / Rights | Open Access / Creative Commons |
| Resource Verification | Listed PDF (Verification Pending) |
| Original Host Website |
HAL Open Science
(hal.science)
|
| File Format | application/pdf (Portable Document Format) |
| Language | EN |
| Catalog ID | DOC-148535 |
| Original Source Link | Visit Source Page on hal.science » |