scholarly journals Spreading in space–time periodic media governed by a monostable equation with free boundaries, Part 2: Spreading speed

2019 ◽  
Vol 36 (6) ◽  
pp. 1539-1573 ◽  
Author(s):  
Weiwei Ding ◽  
Yihong Du ◽  
Xing Liang
Keyword(s):  
Space Time ◽  
Spreading Speed ◽  
Free Boundaries ◽  
Periodic Media ◽  
Monostable Equation ◽  
Time Periodic

Group velocity in space-time periodic media

1971 ◽  
Vol 7 (14) ◽  
pp. 410 ◽  
Author(s):  
R.S. Chu ◽  
T. Tamir
Keyword(s):  
Group Velocity ◽  
Space Time ◽  
Periodic Media ◽  
Time Periodic

scholarly journals Some dependence results between the spreading speed and the coefficients of the space–time periodic Fisher–KPP equation

2011 ◽  
Vol 22 (2) ◽  
pp. 169-185 ◽  
Author(s):  
GRÉGOIRE NADIN
Keyword(s):  
Reaction Diffusion ◽  
Space Time ◽  
Spreading Speed ◽  
Reaction Diffusion Equation ◽  
Dependence Relation ◽  
Kpp Equation ◽  
Minimal Speed ◽  
The Cauchy Problem ◽  
Image Position ◽  
Time Periodic

We investigate in this paper the dependence relation between the space–time periodic coefficients A, q and μ of the reaction–diffusion equation and the spreading speed of the solutions of the Cauchy problem associated with compactly supported initial data. We prove in particular that (1) taking the spatial or temporal average of μ decreases the minimal speed, (2) if μ is not constant with respect to x, then increasing the amplitude of the diffusion matrix A does not necessarily increase the minimal speed and (3) if A = IN, μ is a constant, then the introduction of a space periodic drift term q = ∇Q decreases the minimal speed. In order to prove these results, we use a variational characterisation of the spreading speed that involves a family of periodic principal eigenvalues associated with the linearisation of the equation near zero. We are thus back to the investigation of the dependence relation between this family of eigenvalues and the coefficients.

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