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- Li Chen, Ansgar Jüngel
- SIAM J. Math. Analysis
- 2004

Abstract. The global existence of a non-negative weak solution to a multi-dimensional parabolic strongly coupled model for two competing species is proved. The main feature of the model is that the diffusion matrix is non-symmetric and generally not positive definite and that the non-diagonal matrix elements (the cross-diffusion terms) are allowed to be… (More)

A new approach to the construction of entropies and entropy productions for a large class of nonlinear evolutionary PDEs of even order in one space dimension is presented. The task of proving entropy dissipation is reformulated as a decision problem for polynomial systems. The method is successfully applied to the porous medium equation, the thin film… (More)

- Ansgar Jüngel
- SIAM J. Math. Analysis
- 2010

The global-in-time existence of weak solutions to the barotropic compressible quantum Navier-Stokes equations in a three-dimensional torus for large data is proved. The model consists of the mass conservation equation and a momentum balance equation, including a nonlinear thirdorder differential operator, with the quantum Bohm potential, and a… (More)

- Ansgar Jüngel, René Pinnau
- SIAM J. Math. Analysis
- 2000

A nonlinear fourth-order parabolic equation in one space dimension with periodic boundary conditions is studied. This equation arises in the context of fluctuations of a stationary nonequilibrium interface and in the modeling of quantum semiconductor devices. The existence of global-in-time non-negative weak solutions is shown. A criterion for the… (More)

A coupled quantum drift-diffusion Schrödinger-Poisson model for stationary resonant tunneling simulations in one space dimension is proposed. In the ballistic quantum zone with the resonant quantum barriers, the Schrödinger equation is solved. Near the contacts, where collisional effects are assumed to be important, the quantum drift-diffusion model is… (More)

- Gonzalo Galiano, María L. Garzón, Ansgar Jüngel
- Numerische Mathematik
- 2003

- Pierre Degond, Ansgar Jüngel, Paola Pietra
- SIAM J. Scientific Computing
- 2000

The energy-transport models describe the flow of electrons through a semiconductor crystal, influenced by diffusive, electrical and thermal effects. They consist of the continuity equations for the mass and the energy, coupled to Poisson’s equation for the electric potential. These models can be derived from the semiconductor Boltzmann equation. This paper… (More)

- Ansgar Jüngel, Daniel Matthes
- SIAM J. Math. Analysis
- 2008

The logarithmic fourth-order equation

A one-dimensional transient quantum Euler-Poisson system for the electron density, the current density and the electrostatic potential in bounded intervals is considered. The equations include the Bohm potential accounting for quantum mechanical effects and are of dispersive type. They are used, for instance, for the modeling of quantum semiconductor… (More)