Blow up pro les for a quasilinear reaction-diffusion equation with weighted reaction with linear growth
Fecha
2019
Autores
Título de la revista
ISSN de la revista
Título del volumen
Editor
Springer
Resumen
We study the blow up profiles associated to the following second order reaction–diffusion equation with non-homogeneous reaction: ∂tu=∂xx(um)+|x|σu,with σ> 0. Through this study, we show that the non-homogeneous coefficient | x| σ has a strong influence on the blow up behavior of the solutions. First of all, it follows that finite time blow up occurs for self-similar solutions u, a feature that does not appear in the well known autonomous case σ= 0. Moreover, we show that there are three different types of blow up self-similar profiles, depending on whether the exponent σ is closer to zero or not. We also find an explicit blow up profile. The results show in particular that global blow up occurs when σ> 0 is sufficiently small, while for σ> 0 sufficiently large blow up occurs only at infinity, and we give prototypes of these phenomena in form of self-similar solutions with precise behavior. This work is a part of a larger program of understanding the influence of non-homogeneous weights on the blow up sets and rates. © 2019, Springer Science+Business Media, LLC, part of Springer Nature.
Descripción
Citación
Journal of Dynamics and Differential Equations 31, 2061–2094 (2019)
Colecciones
Excepto si se señala otra cosa, la licencia del ítem se describe como Attribution-NonCommercial-NoDerivatives 4.0 Internacional