Slow motion for one-dimensional nonlinear damped hyperbolic Allen-Cahn systems
| dc.contributor.author | Folino, Raffaele | |
| dc.date.accessioned | 2021-12-06T14:42:00Z | |
| dc.date.available | 2021-12-06T14:42:00Z | |
| dc.date.issued | 2019-10-02 | |
| dc.description.abstract | We consider a nonlinear damped hyperbolic reaction-diffusion system in a bounded interval of the real line with homogeneous Neumann boundary conditions and we study the metastable dynamics of the solutions. Using an "energy approach" introduced by Bronsard and Kohn [11] to study slow motion for Allen-Cahn equation and improved by Grant [25] in the study of Cahn-Morral systems, we improve and extend to the case of systems the results valid for the hyperbolic Allen-Cahn equation (see [18]). In particular, we study the limiting behavior of the solutions as ε → 0+, where ε2 is the diffusion coefficient, and we prove existence and persistence of metastable states for a time Tε > exp(A/ε). Such metastable states have a transition layer structure and the transition layers move with exponentially small velocity. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 21 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Folino, R. (2019). Slow motion for one-dimensional nonlinear damped hyperbolic Allen-Cahn systems. <i>Electronic Journal of Differential Equations, 2019</i>(113), pp. 1-21. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/15007 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2019, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | Hyperbolic reaction-diffusion systems | |
| dc.subject | Allen-Cahn equation | |
| dc.subject | Metastability | |
| dc.subject | Energy estimates | |
| dc.title | Slow motion for one-dimensional nonlinear damped hyperbolic Allen-Cahn systems | en_US |
| dc.type | Article |