A variational property of critical speed to travelling waves in the presence of nonlinear diffusion. (October 2015)

• Record Type: Journal Article
• Authors: Gavioli, Andrea; Sanchez, Luís
• Is Part Of: Applied mathematics letters. Volume 48(2015:Oct.)
• Page Start: 47
• Page End: 54
• Publication Date: 2015-10
• Subjects: Travelling wave -- Nonlinear diffusion -- Critical speed -- Constrained minimum; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2015.03.011
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: Let f be a continuous function in [ 0, 1 ] with f ( 0 ) = 0 = f ( 1 ) and f > 0 on ] 0, 1 [ . We show that, under additional mild conditions on f, the minimal speed for travelling waves of (0.1) ∂ u ∂ t = ∂ ∂ x [ | ∂ u ∂ x | p − 2 ∂ u ∂ x ] + f ( u ), may be computed via a constrained minimum problem which in turn is related to the solution of a singular boundary value problem in the half line.