Uniqueness of travelling waves for nonlocal monostable equations

By Jack Carr, Adam J. J. Chmaj. 2004

325 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/6c023befecbe23c64b1b4f4c6b4b52b1497ae686

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In Computational Theory and Mathematics

In Control and Systems Engineering

In Mathematical Physics

Citations in the corpus

Existence and nonexistence of traveling waves for a nonlocal monostable equation (2008, background): “[3] J. Carr and A. Chmaj, Uniqueness of travelling waves for nonlocal monostable equations, Proc.”
Propagation speed of travelling fronts in non local reaction–diffusion equations (2005, background): “Recently, equality has been obtained by Carr and Chmaj [6] in the case where J has compact support and f (u)= u(1− u).”
Spreading speeds and traveling waves for nonlocal dispersal equations with degenerate monostable nonlinearity (2012, methodology): “For the non-degenerate nonlinearities satisfying the KPP condition, the asymptotic behavior of φ∗(ξ) with critical speed c = c∗ is not purely exponential, but it is a power of |ξ | times an exponential, see [10] for details.”
A logistic equation with refuge and nonlocal diffusion (2009, background): “quote for instance [3], [5], [ 6 ], [8], [15], [16], [18], [19], [32] and [33], devoted to travelling front type solutions to the parabolic problem when › =R, and [4], [9], [10], [17], [31], which dealt with the study of problem (1.2) with a logistic type, bistable or power-like nonlinearity.”
Traveling Fronts in Monostable Equations with Nonlocal Delayed Effects (2008, methodology): “Our method is to firstly establish the exact asymptotic behavior of the profile U (ξ) as ξ → −∞ by using the approach developed by Carr and Chmaj [8] for a nonlocal reaction– diffusion equation, and then obtain the uniqueness by using Theorem 4.”
Nonlocal anisotropic dispersal with monostable nonlinearity (2008, methodology): “Then, Harris, Hudson and Zinner [18] and more recently Carr and Chmaj [4], Chen and Guo [5] and Coville and Dupaigne [11] extended and completed the work of Schumacher to more general monostable nonlinearities and dispersal kernels J satisfying what is called in the literature the Mollison condition”
On uniqueness of semi-wavefronts (2010, methodology): “Now, from the technical point of view our approach to equation (1) differs from the methods used by Diekmann and Kaper, Schumacher and Carr and Chmaj [4] in many key points.”