Publications

Numerical Approximation of Riesz-Feller Operators on R,

with F. de la Hoz and I. Girona, arXiv:2401.07140

Numerical computation of the half Laplacian by means of a fast convolution algorithm

with F. de la Hoz and I. Girona, in ETNA, Volume 60, pp. 59-98, 2024. ArXiv:2306.05009.

A fast convolution method for the fractional Laplacian in R,

with J. Cayama, F. de la Hoz and C. J. Garcia-Cervera, arXiv:2212.05143.

Large time behaviour of a conservation law regularised by a Riesz-Feller operator: the sub-critical case,

with X. Diez. arXiv:2302.03981. Czechoslovak Mathematical Journal, Vol. 73, No. 4, pp. 1057-1080, 2023.

A Pseudospectral Method for the One-Dimensional Fractional Laplacian on R,

with J. Cayama and F. de la Hoz. Applied Mathematics and Computation, Volume 389, 15, (January 2021), 125577. Arxiv:1908.09143

Numerical Approximation of the Fractional Laplacian on R Using Orthogonal Families,

with J. Cayama and F. de la Hoz. Applied Numerical Mathematics, 158, 164-193 (December 2020). Arxiv:2001.08825

Vanishing viscosity limit of a conservation law regularised by a Riesz-Feller operator,

with X. Diez. Monatshefte für Mathematik,192, 513-550 (2020), Arxiv:1909.00685

with H. Knüpfer and J.J.L. Velázquez SIAM J. Math. Anal., 50 (2018), 1900–1917.

Addendum to "Travelling waves for a non-local Korteweg-de Vries-Burgers equation" [J. Differential Equations 257 (2014), no. 3, 720--758],

with F. Achleitner. Journal of Differential Equations, 262 (2017) pp. 1155-1160.

Interfaces determined by capillarity and gravity in a two-dimensional porous medium,

with M. Calle and J.J.L. Velázquez. Interfaces and Free Boundaries, 18 (2016), no. 3, 355--391.

A pseudo-spectral method for a non-local KdV-Burgers equation posed on R,

with F. de la Hoz. J. Comput. Phys. 311 (2016), 45–61

A non-local KdV-Burgers equation: Numerical study of travelling waves.

Commun. Appl. Ind. Math. 6 (2015), no. 2, e-533, 21 pp.

Pattern formation in a pseudo-parabolic equation,

with J.R. King. arXiv:1605.08258

Travelling waves for a non-local Korteweg-de Vries-Burgers equation,

with F. Achleitner and S. Hittmeir. J. Differential Equations 257 (2014), no. 3, 720–758.

Existence of solutions describing accumulation in a thin-film flow (arXiv:1301.0727)

with J.J.L. Velázquez. SIAM J. Appl. Dyn. Syst., 13(1), 47–93 (January 2014).

Fluid accumulation in thin-film flows driven by surface tension and gravity (first part of arXiv:1107.5917, reduced),

with J.J.L. Velázquez. Appl. Math. Letters. Vol. 26, n. 6, pp. 649–653 (June 2013).

Traveling waves of a kinetic transport model for the KPP-Fisher equation,

with S. Hittmeir and C. Schmeiser. SIAM J. Math. Anal. Vol. 44, n. 6, pp. 4128–4146 (Dec. 2012).

Analysis of oscillations in a drainage equation (second part of arXiv:1107.5917, improved),

with J.J.L. Velázquez, SIAM J. Math. Anal. Vol. 44, n. 3, pp. 1588-1616 (May 2012).

Front propagation in a heterogeneous Fisher equation: the homogeneous case is non-generic,

with J.R. King. Q J Mechanics Appl Math.Vol. 63(4). pp. 521-571 (Nov. 2010).

Long-time behaviour of a one-dimensional BGK model: convergence to macroscopic rarefaction waves,

with C. Schmeiser. Monatshefte fuer Mathematik, Vol. 160, n. 4, pp. 361-374 (July 2010).

Weak shocks of a BGK kinetic model relaxing to the isentropic system of gas dynamics,

with S. Hittmeir and C. Schmeiser. Kinetic and Related Models, Vol. 3, n. 2, pp. 255-279 (June 2010).

Linear stability analysis of travelling waves for a pseudo-parabolic Burgers' equation.

Dynamics of PDE, Vol. 7, n. 1, pp.77-105 (March 2010)

Kinetic shock profiles for nonlinear hyperbolic conservation laws,

with S. Hittmeir and C. Schmeiser. Rivista Matematica della Universita' di Parma. Vol. 1, pp. 139-198 (2009) - Serie 8.

Numerical schemes for a pseudo-parabolic Burgers equation: discontinuous data and long-time behaviour,

with I.S. Pop. J. Comput. Appl. Math., Vol. 224, n. 1, pp. 269-283 (Feb. 2009).

Stability of solitary waves in a semiconductor drift-diffusion model,

with C. Schmeiser. SIAM J. Appl. Math. Vol. 68, n. 5, pp. 1423--1438 (2008).

A note on L1 stability of travelling waves for a one-dimensional BGK model.

Hyperbolic Problems: Theory, Numerics, Applications, proceedings of the 11th international conference on hyperbolic problems, Lyon, 2006, 431--438, Springer (2008).

Kinetic profiles for shock waves of scalar conservation laws,

with C. Schmeiser, Bull. Inst. Math. Acad. Sin. (N.S.) 2 (2007), no. 2, 391--408.

Weak shocks for a one-dimensional BGK kinetic model for conservation laws,

with C. Schmeiser. SIAM J. Math. Anal. 38 (2006), no. 2, 637--656.

Small- and waiting-time behaviour of a Darcy flow model with a dynamic pressure saturation relation,

with J.R. King. SIAM J. Appl. Math. 66 (2006), no. 5, 1482--1511. Extended version

Non-classical shocks for Buckley-Leverett: degenerate pseudo-parabolic regularisation,

with C.J. van Duijn and I.S. Pop. Progress in industrial mathematics at ECMI 2004, 569--573, Math. Ind., 8, Springer, Berlin, 2006.

Pseudo-parabolic equations with driving convection term.

My thesis (March 2003)

A model problem for groundwater flow with dynamic capillary pressure: stability of travelling waves,

with J. Hulshof. Nonlinear Anal. TMA, 52, 1199-1218 (2003),

Infiltration in Porous Media with Dynamic Capillary Pressure: Travelling Waves,

with C.J. van Duijn and J. Hulshof. Eur. J. Appl. Math. 11, 381-397 (2000).