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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]

This paper concerns with a compact network model combined with distributed models for semiconductor devices. For linear RLC networks containing distributed semiconductor devices, we construct a mathematical model that joins the differential‐algebraic initial value problem for the electric circuit with multidimensional parabolic‐elliptic boundary value problems for the devices. We prove an existence and uniqueness result and the asymptotic behavior of this mixed initial boundary value problem of partial differential‐algebraic equations. [ABSTRACT FROM AUTHOR]