The principal eigenvalue of a space–time periodic parabolic operator

2008 ◽  
Vol 188 (2) ◽  
pp. 269-295 ◽  
Author(s):  
Gregoire Nadin
Keyword(s):  
Principal Eigenvalue ◽  
Space Time ◽  
Parabolic Operator ◽  
Time Periodic

scholarly journals Monotonicity of the principal eigenvalue for a linear time-periodic parabolic operator

2019 ◽  
Vol 147 (12) ◽  
pp. 5291-5302 ◽  
Author(s):  
Shuang Liu ◽  
Yuan Lou ◽  
Rui Peng ◽  
Maolin Zhou
Keyword(s):  
Linear Time ◽  
Principal Eigenvalue ◽  
Parabolic Operator ◽  
Time Periodic

Protection Zones in Periodic-Parabolic Problems

2020 ◽  
Vol 20 (2) ◽  
pp. 253-276
Author(s):  
Julián López-Gómez
Keyword(s):  
Mixed Type ◽  
Principal Eigenvalue ◽  
Boundary Operator ◽  
General Boundary ◽  
Parabolic Problems ◽  
Parabolic Operator ◽  
Protection Zones ◽  
Competitive Environments

AbstractThis paper characterizes whether or not\Sigma_{\infty}\equiv\lim_{\lambda\uparrow\infty}\sigma[\mathcal{P}+\lambda m(% x,t),\mathfrak{B},Q_{T}]is finite, where {m\gneq 0} is T-periodic and {\sigma[\mathcal{P}+\lambda m(x,t),\mathfrak{B},Q_{T}]} stands for the principal eigenvalue of the parabolic operator {\mathcal{P}+\lambda m(x,t)} in {Q_{T}\equiv\Omega\times[0,T]} subject to a general boundary operator of mixed type, {\mathfrak{B}}, on {\partial\Omega\times[0,T]}. Then this result is applied to discuss the nature of the territorial refuges in periodic competitive environments.

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