Estimates for the principal spectrum point for certain time-dependent parabolic operators

By V. Hutson, Wenxian Shen, G. Vickers. 2000

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The principal eigenvalue of a space–time periodic parabolic operator (2009, background): “In the other hand, many studies have been carried out on time-periodic parabolic operator in bounded domains (see [15–17]).”
Effects of diffusion and advection on the principal eigenvalue of a periodic-parabolic problem with applications (2015, background): “refer to [14,18,19,37,40,48,50]; on the other hand, the study on the principal eigenvalue for cooperative systems can be found in [2–4,12,13,15] and the references therein.”
Spectral Theory for Random and Nonautonomous Parabolic Equations and Applications (2008, background): “Principal spectrum for nonautonomous parabolic equations defined for all t ∈ R is well studied in several works (see [9–12, 14–18, 21], and references therein) and has also found great applications (see [8, 13, 19, 22, 27], etc.”
Reaction-diffusion-advection models for the effects and evolution of dispersal (2013, unknown): “In [52], the authors show that ρ0 ≤ ρ̂0 where ρ0 and ρ̂0 are the principal eigenvalues of ∂ψ/∂t−A(t)ψ = ρψ in Ω× R, Bψ = 0 on ∂Ω× R”
Convergence in monotone and uniformly stable skew-product semiflows with applications (2005, background): “According to [18], there exists a unique principal spectrum point l dð Þ;mð Þ associated with the following linear almost periodic parabolic problem”