Local sensing and nonlinear diffusion in models of chemotactic aggregation
By Ariane Trescases
Spatial mean-field models in neuroscience and the modelling of noisy grid cells
By Pierre Roux
By Zoe Wyatt
Appears in collection : Mathematical aspects of the physics with non-self-adjoint operators / Les aspects mathématiques de la physique avec les opérateurs non-auto-adjoints
On a background Minkowski spacetime, the Euler equations (both relativistic and not) are known to admit unstable homogeneous solutions with finite-time shock formation. Such shock formation can be suppressed on cosmological spacetimes whose spatial slices expand at an accelerated rate. However, situations with decelerated expansion, which are relevant in our early universe, are not as well understood. I will present some recent joint work in this direction, based on collaborations with David Fajman, Maciej Maliborski, Todd Oliynyk and Max Ofner.