Ansgar Jüngel

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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)
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)
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)
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)
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)