Doctor en Ciencias de la Ingeniería, Mención Modelación Matemática / This thesis deals with two different problems: in the first one, we study the large-time behavior of solutions of one-dimensional fractional Fisher-KPP reaction diffusion equations, when the initial condition is asymptotically front-like and it decays at infinity more slowly than a power x^b, where b < 2\alpha and \alpha\in (0,1) is the order of the fractional Laplacian (Chapter 2); in the second problem, we study the time asymptotic propagation of solutions to the fractional reaction diffusion cooperative systems (Chapter 3).
For the first problem, we prove that the level sets of the solutions move exponentially fast as time goes to infinity. Moreover, a quantitative estimate of motion of the level sets is obtained in terms of the decay of the initial condition.
In the second problem, we prove that the propagation speed is exponential in time, and we find a precise exponent depending on the smallest index of the fractional laplacians and of the nonlinearity, also we note that it does not depend on the space direction.
| Identifer | oai:union.ndltd.org:UCHILE/oai:repositorio.uchile.cl:2250/115538 |
| Date | January 2014 |
| Creators | Yangari Sosa, Miguel Ángel |
| Contributors | Felmer Aichele, Patricio, Roquejoffre, Jean-Michel, Facultad de Ciencias Físicas y Matemáticas, Departamento de Ingeniería Matemática, García-Huidobro Campos, Marta, Sire, Yannick |
| Publisher | Universidad de Chile |
| Source Sets | Universidad de Chile |
| Language | English |
| Detected Language | English |
| Type | Tesis |
| Rights | Attribution-NonCommercial-NoDerivs 3.0 Chile, http://creativecommons.org/licenses/by-nc-nd/3.0/cl/ |
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