Uniqueness and stability properties of monostable pulsating fronts

By François Hamel, Lionel Roques. 2011

119 citations recorded by the source corpus.

Subfields: Modeling and Simulation, Public Health, Environmental and Occupational Health, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/76054ceea34fde6a8a75d19972c9bb2231c2e2fa

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Citations in the corpus

Convergence to a single wave in the Fisher-KPP equation (2016, background): “Then there is a minimal speed c∗ > 0 such that for each c ≥ c∗, there is a unique pulsating front Uc(t, x), up to a time shift [4, 13].”
Pulsating fronts for nonlocal dispersion and KPP nonlinearity (2013, unknown): “Within this framework, Xin [62, 63] has proved existence and uniqueness up to translation of pulsating fronts for equation (1.2) with a homogeneous bistable or ignition non-linearity.”
Generalized Transition Waves and Their Properties (2010, background): “t can for instance be dened as t = x2RN; (xe ct) >0 : The general denitions that we just gave also generalize the classical notions of pulsating traveling fronts in spatially periodic media (see [2, 5, 6, 8, 16, 20, 23, 39, 43, 44]) with possible periodicity or almost-periodicity in time (see [14”
Bistable pulsating fronts for reaction-diffusion equations in a periodic habitat (2014, methodology): “Furthermore, some variational formulas for cL in the positive case and in the more specific KPP case have been derived in [10, 12, 20] and some further qualitative and uniqueness properties for each speed c ∈ [cL,+∞) have been given in [25, 28, 29].”
Traveling waves and spreading speeds for time-space periodic monotone systems (2015, background): “Hamel and Roques [14] gave a complete classification of all KPP pulsating fronts and obtained some global stability properties for the fronts including the one with minimal speed.”
Fast propagation for KPP equations with slowly decaying initial conditions (2009, background): “ng fronts in inﬁnite cylinders with shear ﬂows has been shown in [30], the convergence to pulsating traveling fronts for reactiondiﬀusion-advection equations in periodic media has been established in [17]. Further estimates about the ﬁnite spreading speeds associated with compactly supported or expo”
Time periodic traveling wave solutions for periodic advection–reaction–diffusion systems (2014, unknown): “In Section 4, under the same conditions presented in Section 3, we utilize similar methods as in Hamel and Roques [17] and Zhao and Ruan [37] to study the asymptotic stability of the time periodic traveling wave solution of (1.”