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- Carlota M. Cuesta, Christian Schmeiser
- SIAM J. Math. Analysis
- 2006

For one-dimensional kinetic BGK models, regarded as relaxation models for scalar conservation laws with genuinely nonlinear fluxes, existence of small amplitude travelling waves is proven. Dynamicâ€¦ (More)

- Carlota M. Cuesta, Sabine Hittmeir, Christian Schmeiser
- SIAM J. Math. Analysis
- 2012

A reactive kinetic transport equation whose macroscopic limit is the KPP-Fisher equation is considered. In a scale, where collisions occur at a faster rate than reactions, existence of travelingâ€¦ (More)

We consider a simplified model for vertical non-stationary groundwater flow, which includes dynamic capillary pressure effects. Specifically, we consider a viscous Burgersâ€™â€“type equation that isâ€¦ (More)

- John R. King, Carlota M. Cuesta
- SIAM Journal of Applied Mathematics
- 2006

We address the small-time evolution of interfaces (fronts) for the pseudoparabolic generalization âˆ‚u âˆ‚t = âˆ‚ âˆ‚x ( u âˆ‚u âˆ‚x + u âˆ‚2u âˆ‚xâˆ‚t ) of the porous-medium equation, identifying regimes in which theâ€¦ (More)

A unified framework for studying the existence and stability of kinetic shock profiles is presented. This includes small amplitude waves for the situation when the macroscopic model is a hyperbolicâ€¦ (More)

We investigate the linear stability of non-monotone travelling wave solutions of the pseudo-parabolic Burgersâ€™ type equation âˆ‚u âˆ‚t = âˆ‚u âˆ‚x2 + 2 u âˆ‚u âˆ‚x + Ï„ âˆ‚u âˆ‚x2âˆ‚t with Ï„ > 0 . The monotonicity ofâ€¦ (More)

For one-dimensional kinetic BGK models, regarded as relaxation models for scalar conservation laws with genuinely nonlinear fluxes, we prove that the macroscopic density converges to the rarefactionâ€¦ (More)

- Carlota M. Cuesta, J. J. L. VelÃ¡zquez
- SIAM J. Applied Dynamical Systems
- 2014

We consider a third order non-autonomous ODE that arises as a model of fluid accumulation in a two dimensional thin-film flow driven by surface tension and gravity. With the appropriate matchingâ€¦ (More)

- Carlota M. Cuesta, Christian Schmeiser
- SIAM Journal of Applied Mathematics
- 2008

We consider a macroscopic (drift-diffusion) model describing a simple microwave generator, consisting of a special type of semiconductor material that, when biased above a certain threshold voltage,â€¦ (More)

- Carlota M. Cuesta, Hans KnÃ¼pfer, Juan J. L. VelÃ¡zquez
- SIAM J. Math. Analysis
- 2018