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On the age-dependent predator-prey model

Antoni Leon Dawidowicz, Anna Poskrobko, Jerzy Leszek Zalasiński (2011)

Applicationes Mathematicae

The paper deals with the description of a model which is the synthesis of two classical models, the Lotka-Volterra and McKendrick-von Foerster models. The existence and uniqueness of the solution for the new population problem are proved, as well the asymptotic periodicity but under some simplifying assumptions.

Viscous Shock Capturing in a Time-Explicit Discontinuous Galerkin Method

A. Klöckner, T. Warburton, J. S. Hesthaven (2011)

Mathematical Modelling of Natural Phenomena

We present a novel, cell-local shock detector for use with discontinuous Galerkin (DG) methods. The output of this detector is a reliably scaled, element-wise smoothness estimate which is suited as a control input to a shock capture mechanism. Using an artificial viscosity in the latter role, we obtain a DG scheme for the numerical solution of nonlinear systems of conservation laws. Building on work by Persson and Peraire, we thoroughly justify the...

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