Exponentially slow motion for a one-dimensional Allen-Cahn equation with memory
Por:
Folino R.
Publicada:
1 ene 2021
Resumen:
A reaction-diffusion equation with memory kernel of Jeffreys type and with a balanced bistable reaction term is considered in a bounded interval of the real line. Taking advantage of the fact that in this case the integro-differential equation can be transformed into a local partial differential equation, it is proved that there exist solutions which evolve very slowly in time and maintain a transition layer structure for an exponentially long time T? = c1 exp(c2/?) as ? ? 0+, where ?2 is the diffusion coefficient. Hence, we extend to reaction-diffusion equations with memory kernel of Jeffreys type the well-known results valid for the classic Allen-Cahn equation. © The Author(s) 2021.
Filiaciones:
Folino R.:
Departamento de Matemáticas y Mecánica, Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, Circuito Escolar s/n, Ciudad Universitaria C.P., Cd. Mx., 04510, Mexico
|