Accelerated nonlocal nonsymmetric dispersion for monostable equations on the real line. Issue 4 (12th March 2019)

• Record Type: Journal Article
• Authors: Finkelshtein, Dmitri; Tkachov, Pasha
• Is Part Of: Applicable analysis. Volume 98:Issue 4(2019)
• Page Start: 756
• Page End: 780
• Publication Date: 2019-03-12
• Subjects: Nonlocal diffusion -- reaction–diffusion equation -- front propagation -- acceleration -- monostable equation -- nonlocal nonlinearity -- long-time behaviour -- integral equation; 35B40 -- 35K57 -- 47G20 -- 45G10; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2017.1400537
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: We consider the accelerated propagation of solutions to equations with a nonlocal linear dispersion on the real line and monostable nonlinearities (both local or nonlocal, however, not degenerated at 0), in the case when either of the dispersion kernel or the initial condition has regularly heavy tails at both± ∞, perhaps different. We show that, in such case, the propagation to the right direction is fully determined by the right tails of either the kernel or the initial condition. We describe both cases of integrable and monotone initial conditions which may give different orders of the acceleration. Our approach is based, in particular, on the extension of the theory of sub-exponential distributions, which we introduced early.