TWAROGOWSKA , Monika

The Phd thesis is devoted to the numerical and mathematical analysis of systems of partial differential equations arising in the modeling of cells movement. The model of nutrient-dependent tumour growth is built and the asymptotic stability of constant steady states for small perturbations is proved. Then the parabolic and hyperbolic models of...

We consider two models which were both designed to describe the movement of eukaryotic cells responding to chemical signals. Besides a common standard parabolic equation for the diffusion of a chemoattractant, like chemokines or growth factors, the two models differ for the equations describing the movement of cells. The first model is based on...

We analyze numerically two macroscopic models of crowd dynamics: the classical Hughes model and the second order model being an extension to pedestrian motion of the Payne-Whitham vehicular traffic model. The desired direction of motion is determined by solving an eikonal equation with density dependent running cost, which results in...

We consider two models which were both designed to describe the movement of eukaryotic cells responding to chemical signals. Besides a common standard parabolic equation for the diffusion of a chemoattractant, like chemokines or growth factors, the two models differ for the equations describing the movement of cells. The first model is based on...

We analyze numerically two macroscopic models of crowddynamics: the classical Hughes model and the second order model beingan extension to pedestrian motion of the Payne-Whitham vehiculartraffic model. The desired direction of motion is determined by solvingan eikonal equation with density dependent running cost, which resultsin minimization of...

We analyze numerically macroscopic models of crowd dynamics: classical Hughes model and the second order model being an extension to pedestrian motion of the Payne-Whitham vehicular traffic model. The desired direction of motion is determined by solving an eikonal equation with density dependent running cost function standing for minimization...

We analyze numerically two macroscopic models of crowd dynamics: the classical Hughes model and the second order model being an extension to pedestrian motion of the Payne-Whitham vehicular traffic model. The desired direction of motion is determined by solving an eikonal equation with density dependent running cost, which results in...

We analyze numerically some macroscopic models of pedestrian motion to compare their capabilities of reproducing characteristic features of crowd behavior, such as travel times minimization and crowded zones avoidance, as well as complex dynamics like stop-and-go waves and clogging at bottlenecks. We compare Hughes' model with different running...

We introduce a numerical scheme to approximate a quasi-linear hyperbolic system which models the movement of cells under the influence of chemotaxis. Since we expect to find solutions which contain vacuum parts, we propose an upwinding scheme which handles properly the presence of vacuum and, besides, which gives a good approximation of the...