33 citations · 200 across the 20 of their papers we have counts for
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math.AP2017★ 5 cited
Asymptotic stability of traveling wave solutions for nonlocal viscous conservation laws with explicit decay rates
Franz Achleitner, Yoshihiro Ueda
We consider scalar conservation laws with nonlocal diffusion of Riesz-Feller type such as the fractal Burgers equation. The existence of traveling wave solutions with monotone decr…
math.AP2017★ 26 cited
On multi-dimensional hypocoercive BGK models
Franz Achleitner, Anton Arnold, Eric A. Carlen
We study hypocoercivity for a class of linearized BGK models for continuous phase spaces. We develop methods for constructing entropy functionals that enable us to prove exponentia…
math.AP2017
Two classes of nonlocal Evolution Equations related by a shared Traveling Wave Problem
Franz Achleitner
We consider reaction-diffusion equations and Korteweg-de Vries-Burgers (KdVB) equations, i.e. scalar conservation laws with diffusive-dispersive regularization. We review the exist…