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EnglishWe study a class of systems of reaction-diffusion equations in infinite cylinders which arise within the context of Ginzburg-Landau theories and describe the kinetics of phase transformation in second-order or weakly first-order phase transitions with non-conserved order parameters. We use a variational characterization to study the existence of a special class of traveling wave solutions which are characterized by a fast exponential decay in the direction of propagation. Our main result is a simple verifiable criterion for existence of these traveling waves under the very general assumptions of non-linearities. We also prove boundedness, regularity, and some other properties of the obtained solutions, as well as several sufficient conditions for existence or non-existence of such traveling waves, and give rigorous upper and lower bounds for their speed. In addition, we prove that the speed of the obtained solutions gives a sharp upper bound for the propagation speed of a class of disturbances which are initially sufficiently localized. We give a sample application of our results using a computer-assisted approach.
| Autori interni: | ||
| Autori: | LUCIA M; MURATOV C; NOVAGA M. | |
| Titolo: | Existence of traveling waves of invasion for Ginzburg-Landau-type problems in infinite cylinders | |
| Anno del prodotto: | 2008 | |
| Digital Object Identifier (DOI): | 10.1007/s00205-007-0097-x | |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
File in questo prodotto:
http://hdl.handle.net/11568/119024
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