Metastable patterns for a reaction-diffusion model with mean curvature-type diffusion
Por:
Folino, Raffaele, Plaza, Ramon G., Strani, Marta
Publicada:
1 ene 2021
Ahead of Print:
1 ene 2020
Resumen:
Reaction-diffusion equations are widely used to describe a variety of phenomena such as pattern formation and front propagation in biological, chemical and physical systems. In the one-dimensional model with a balanced bistable reaction function, it is well-known that there is persistence of metastable patterns for an exponentially long time, i.e. a time proportional to exp?(C/e) where C,e are strictly positive constants and e2 is the diffusion coefficient. In this paper, we extend such results to the case when the linear diffusion flux is substituted by the mean curvature operator both in Euclidean and Lorentz–Minkowski spaces. More precisely, for both models, we prove existence of metastable states which maintain a transition layer structure for an exponentially long time and we show that the speed of the layers is exponentially small. Numerical simulations, which confirm the analytical results, are also provided. © 2020 Elsevier Inc.
Filiaciones:
Folino, Raffaele:
Departamento de Matemáticas y Mecánica, Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, Circuito Escolar s/n, C.P. 04510 Cd. Mx., Ciudad Universitaria, Mexico
Univ Nacl Autonoma Mexico, Inst Invest Matemat Aplicadas & Sistemas, Dept Matemat & Mecan, Circuito Escolar S-N,Ciudad Univ, Mexico City 04510, DF, Mexico
Plaza, Ramon G.:
Departamento de Matemáticas y Mecánica, Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, Circuito Escolar s/n, C.P. 04510 Cd. Mx., Ciudad Universitaria, Mexico
Univ Nacl Autonoma Mexico, Inst Invest Matemat Aplicadas & Sistemas, Dept Matemat & Mecan, Circuito Escolar S-N,Ciudad Univ, Mexico City 04510, DF, Mexico
Strani, Marta:
Dipartimento di Scienze Molecolari e Nanosistemi, Università Ca' Foscari Venezia Mestre, Campus Scientifico, Via Torino 155, Venezia Mestre, 30170, Italy
Univ Ca Foscari Venezia Mestre, Dipartimento Sci Mol & Nanosistemi, Campus Sci,Via Torino 155, I-30170 Venice, Italy
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