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A reaction–diffusion system governing the predator–prey interaction with specialist predator and herd behavior for prey is investigated. Linear stability of the interior equilibrium is studied, and conditions guaranteeing the occurrence of Turing instability, induced by cross‐diffusion, are found, with a full characterization of the Turing instability region in the parameter space. Numerical simulations on the obtained results are provided. [ABSTRACT FROM AUTHOR]

We derive a quantum-corrected hydrodynamic and drift-diffusion model for the out-of-equilibrium particle dynamics in the presence of particle collisions, modeled by a BGK collision term. The quantum mechanical corrections are obtained within the Liouville formalism and are expressed by an effective nonlinear force. The Boltzmann and Fermi-Dirac statistics are included. [ABSTRACT FROM AUTHOR]

In refined network analysis, a compact network model is coupled with distributed models for interconnects and semiconductor devices, linking differential-algebraic equations to partial differential equations, thus creating PDAEs. This paper deals with linear RLC networks containing one-dimensional diodes as distributed devices, modeled by the stationary drift-diffusion equations. For the resulting mixed initial boundary value problem we prove a uniqueness result for solutions close to equilibrium, i.e., with small initial data and electrical sources, based on a contraction argument. [ABSTRACT FROM AUTHOR]