Elliptic Eigenvalue Problems with Large Drift and Applications to Nonlinear Propagation Phenomena

By Henri Berestycki, François Hamel, Nikolai Nadirashvili. 2005

160 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/df07bc813cfa09aba9d877ba125efddc8c9d5cc2

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In Applied Mathematics

In Computational Theory and Mathematics

In Numerical Analysis

Citations in the corpus

Effects of diffusion and advection on the principal eigenvalue of a periodic-parabolic problem with applications (2015, methodology): “To analyze the qualitative behavior of the principal eigenvalue for the elliptic operators mentioned above, the mathematical approaches developed in [5,10,11] rely heavily on the variational characterization of the principal eigenvalue.”
On the Euler equations of incompressible fluids (2007, methodology): “Strong rapid effects are studied using PDE methods ([ 17 ], [50], [55]).”
Enhanced Dissipation and Inviscid Damping in the Inviscid Limit of the Navier–Stokes Equations Near the Two Dimensional Couette Flow (2014, methodology): “The work of [21] considers in a more general framework the connection between the spectral properties of the background flow and the enhanced dissipation effect in the context of passive tracers using the RAGE theorem (see also [11] for the elliptic case).”
Principal eigenvalue and eigenfunctions of an elliptic operator with large advection and its application to a competition model (2008, background): “Among other things, connections between the limit of the principal eigenvalue and the first integrals of the velocity field v are established in [2].”
On the Loss of Continuity for Super-Critical Drift-Diffusion Equations (2012, background): “first eigenvalue estimates [3], mixing rates [11], and expected exit times [24].”
Rearrangement inequalities and applications to isoperimetric problems for eigenvalues (2006, background): “(1)We refer to [13] for a detailed analysis of the behavior of λ1(Ω, A,Bv, V ) when B → +∞ and v is a fixed divergence free vector field in L∞(Ω).”
Enhanced Dissipation, Hypoellipticity, and Anomalous Small Noise Inviscid Limits in Shear Flows (2015, background): “A number of works also focus on estimating the spectrum of the elliptic operator u · ∇ − ν∆, in particular, see [11, 48] and the references therein.”
Analysis of the periodically fragmented environment model: II—biological invasions and pulsating travelling fronts (2005, background): “Some lower and upper bounds for the minimal speed when the advection term v is large are given in [2, 3, 6 , 12, 19, 24].”