[图书][B] Entropy methods for diffusive partial differential equations
A Jüngel - 2016 - Springer
The concept of entropy is a powerful tool not only in physics and chemistry but also in
mathematics. Entropies allow for the development of new techniques to analyze partial …
mathematics. Entropies allow for the development of new techniques to analyze partial …
The boundedness-by-entropy method for cross-diffusion systems
A Jüngel - Nonlinearity, 2015 - iopscience.iop.org
The global-in-time existence of bounded weak solutions to a large class of physically
relevant, strongly coupled parabolic systems exhibiting a formal gradient-flow structure is …
relevant, strongly coupled parabolic systems exhibiting a formal gradient-flow structure is …
Generalizing the Keller–Segel model: Lyapunov functionals, steady state analysis, and blow-up results for multi-species chemotaxis models in the presence of …
D Horstmann - Journal of nonlinear science, 2011 - Springer
In this paper we extend the famous Keller–Segel model for the chemotactic movement of
motile species to some multi-species chemotaxis equations. The presented multi-species …
motile species to some multi-species chemotaxis equations. The presented multi-species …
Mean field games with nonlinear mobilities in pedestrian dynamics
In this paper we present an optimal control approach modeling fast exit scenarios in
pedestrian crowds. In particular we consider the case of a large human crowd trying to exit a …
pedestrian crowds. In particular we consider the case of a large human crowd trying to exit a …
Inverse problems in ion channel modelling
M Burger - Inverse Problems, 2011 - iopscience.iop.org
This paper reviews several inverse problems related to biological ion channels and polymer
nanopores. Different problems arise at different scales and thus lead to different inversion …
nanopores. Different problems arise at different scales and thus lead to different inversion …
[HTML][HTML] The impact of phenotypic switching on glioblastoma growth and invasion
P Gerlee, S Nelander - PLoS computational biology, 2012 - journals.plos.org
The brain tumour glioblastoma is characterised by diffuse and infiltrative growth into
surrounding brain tissue. At the macroscopic level, the progression speed of a glioblastoma …
surrounding brain tissue. At the macroscopic level, the progression speed of a glioblastoma …
Excluded-volume effects in the diffusion of hard spheres
M Bruna, SJ Chapman - Physical Review E—Statistical, Nonlinear, and Soft …, 2012 - APS
Excluded-volume effects can play an important role in determining transport properties in
diffusion of particles. Here, the diffusion of finite-sized hard-core interacting particles in two …
diffusion of particles. Here, the diffusion of finite-sized hard-core interacting particles in two …
Gradient structures and geodesic convexity for reaction–diffusion systems
We consider systems of reaction–diffusion equations as gradient systems with respect to an
entropy functional and a dissipation metric given in terms of a so-called Onsager operator …
entropy functional and a dissipation metric given in terms of a so-called Onsager operator …
[HTML][HTML] Analysis of degenerate cross-diffusion population models with volume filling
A class of parabolic cross-diffusion systems modeling the interaction of an arbitrary number
of population species is analyzed in a bounded domain with no-flux boundary conditions …
of population species is analyzed in a bounded domain with no-flux boundary conditions …
Diffusion of multiple species with excluded-volume effects
M Bruna, SJ Chapman - The Journal of chemical physics, 2012 - pubs.aip.org
Stochastic models of diffusion with excluded-volume effects are used to model many
biological and physical systems at a discrete level. The average properties of the population …
biological and physical systems at a discrete level. The average properties of the population …