| Abstract: |
| Diffusion models appear in multiple sciences such as biology, physics or even economics. They come up naturally as a broad class of natural processes and, in some cases, such as the propagation of a pathogen, the particles may jump long distances in each instant of time thanks to various means of transport. We call this non-local diffusion, and it is modeled by operators such as those of the type $J\ast u - u$, where the kernel $J$ is a density function of the probability of jumps happening.
The phenomenon of quenching in a dynamical system consists of the explosion of the velocity of the solution while the solution itself remains bounded. This phenomenon appears naturally in physical models such as the nonlinear heat conduction in solid hydrogen or the Arrhenius Law in combustion theory.
The aim of this talk is to speak about our study of a system of equations with weakly coupled singular absorption terms and a non-local diffusion operator and the quenching phenomena that arises. We will show our results about the system, which tackle the appearance of stationary solutions, the quenching rates of both components and the possibility of both components presenting quenching at the same time. |
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