14 citations · 24 across the 13 of their papers we have counts for
6 papers · 1 filter
Large time behaviour of a conservation law regularised by a Riesz-Feller operator: the sub-critical case
Carlota M. Cuesta, Xuban Diez
We study the large time behaviour of the solutions of a non-local regularisation of a scalar conservation law. This regularisation is given by a fractional derivative of order $1+α…
Vanishing viscosity limit of a conservation law regularised by a Riesz-Feller operator
Carlota M. Cuesta, Xuban Diez
We study a nonlocal regularisation of a scalar conservation law given by a fractional derivative of order between one and two. The nonlocal operator is of Riesz-Feller type with sk…
Pattern formation in a pseudo-parabolic equation
C. M. Cuesta, J. R. King
We address the propagation into an unstable state of a localised disturbance in a forward-backward diffusion pseudo-parabolic equation. Three asymptotic regimes are distinguished a…
Addendum to "Travelling waves for a non-local Korteweg-de Vries-Burgers equation" [J. Differential Equations 257 (2014), no. 3, 720--758]
Carlota M. Cuesta, Franz Achleitner
We add a theorem to [J. Differential Equations 257 (2014), no. 3, 720--758] by F. Achleitner, C.M. Cuesta and S. Hittmeir. In that paper we studied travelling wave solutions of a K…
Interfaces determined by capillarity and gravity in a two-dimensional porous medium
Maria Calle, Carlota M. Cuesta, Juan J. L. Velazquez
We consider a two-dimensional model of a porous medium where circular grains are uniformly distributed in a squared container. We assume that such medium is partially filled with w…
Fluid accumulation in thin-film fl ows driven by surface tension and gravity (I): Rigorous analysis of a drainage equation
C. M. Cuesta, J. J. L. Velazquez
We derive a boundary layer equation describing accumulation regions within a thin-film approximation framework where gravity and surface tension balance. As part of the analysis of…