Variational principles and the shift in the front speed due to a cutoff.
We apply variational principles to reaction-diffusion equations in order to predict, for a general reaction term, the sign of the shift in the front speed due to a cutoff. We develop an improved variational principle to obtain the shift in the front speed for a wide range of reaction terms, and the theoretical results so obtained are in excellent agreement with numerical solutions. This work proves that variational principles are an optimal framework to deal with fronts propagating into unstable and metastable states under cutoff.
Méndez
Vicenç
V
Departament de Medicina, Facultat de Ciències de la Salut, Universitat Internacional de Catalunya, c/ Josep Trueta s/n, E-08190 Sant Cugat del Vallès (Barcelona) Spain.
Campos
Daniel
D
Zemskov
Evgeny P
EP