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On the method of moving planes and the sliding method
The method of moving planes and the sliding method are used in proving monotonicity or symmetry in, say, thex1 direction for solutions of nonlinear elliptic equationsF(x, u, Du, D2u)=0 in a bounded…
The principal eigenvalue and maximum principle for second‐order elliptic operators in general domains
Nonlinear scalar field equations, I existence of a ground state
1. The Main Result; Examples . . . . . . . . . . . . . . . . . . . . . . . 316 2. Necessary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . 319 3. The Constrained Minimization Method .…
Front propagation in periodic excitable media
This paper is devoted to the study of pulsating travelling fronts for reaction‐diffusion‐advection equations in a general class of periodic domains with underlying periodic diffusion and velocity…
Travelling fronts in cylinders
Further qualitative properties for ellip-tic equations in unbounded domains
L’accès aux archives de la revue « Annali della Scuola Normale Superiore di Pisa, Classe di Scienze » (http://www.sns.it/it/edizioni/riviste/annaliscienze/) implique l’accord avec les conditions…
Computing the implied volatility in stochastic volatility models
The Black-Scholes model [6, 23] has gained wide recognition on financial markets. One of its shortcomings, however, is that it is inconsistent with most observed option prices. Although the model can…
Can a Species Keep Pace with a Shifting Climate?
- H. Berestycki, O. Diekmann, C. J. Nagelkerke, P. Zegeling
- Environmental ScienceBulletin of mathematical biology
- 9 December 2008
The results show that mobility can both reduce and enhance the ability to track climate change that a narrow range can severely reduce this ability and that population range and total population size can both increase and decrease under a moving climate.
Analysis of the periodically fragmented environment model: II—biological invasions and pulsating travelling fronts
Bistable traveling waves around an obstacle
We consider traveling waves for a nonlinear diffusion equation with a bistable or multistable nonlinearity. The goal is to study how a planar traveling front interacts with a compact obstacle that is…