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Full-Text Articles in Physical Sciences and Mathematics
The Positive Solutions Of The Matukuma Equation And The Problem Of Finite Radius And Finite Mass, Jurgen Batt, Yi Li
The Positive Solutions Of The Matukuma Equation And The Problem Of Finite Radius And Finite Mass, Jurgen Batt, Yi Li
Yi Li
This work is an extensive study of the 3 different types of positive solutions of the Matukuma equation 1r2(r2ϕ′)′=−rλ−2(1+r2)λ/2ϕp,p>1,λ>0 : the E-solutions (regular at r = 0), the M-solutions (singular at r = 0) and the F-solutions (whose existence begins away from r = 0). An essential tool is a transformation of the equation into a 2-dimensional asymptotically autonomous system, whose limit sets (by a theorem of H. R. Thieme) are the limit sets of Emden–Fowler systems, and serve as to characterizate the different solutions. The emphasis lies on the study of the M-solutions. …
Existence Of Traveling Wave Solutions For A Nonlocal Reaction-Diffusion Model Of Influenza A Drift, Joaquin Riviera, Yi Li
Existence Of Traveling Wave Solutions For A Nonlocal Reaction-Diffusion Model Of Influenza A Drift, Joaquin Riviera, Yi Li
Yi Li
In this paper we discuss the existence of traveling wave solutions for a nonlocal reaction-diffusion model of Influenza A proposed in Lin et. al. (2003). The proof for the existence of the traveling wave takes advantage of the different time scales between the evolution of the disease and the progress of the disease in the population. Under this framework we are able to use the techniques from geometric singular perturbation theory to prove the existence of the traveling wave.