The idea of this seminar is to bring together local and international experts in the field of partial differential equations (PDE) and related fields. In the talks we want to cover various aspects of PDE and their applications, including modeling, mathematical analysis and numerics. Our goal is to increase the visibility of work that is being done in the field of PDE across the different groups at DIAM and to serve as a meeting platform within the department.
The seminar takes place on Thursdays at 4pm.
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Meer info over webcal.
22 februari 2024 16:00 t/m 17:00
[PDE&A] King Ming Lam: On the stability of starsA fundamental model of a self-gravitating star is given by the Euler-Poisson equation in the setting of a free boundary problem. At the mass critical index, there exists a known class of spherically symmetric (self-similarly) expanding solutions, called the Goldreich-Weber solutions, modelling expanding stars. We establish non-radial non-linear stability of this class of solutions, extending existing results on radial stability. In doing so, we proved global-in-time existence for a larger class of expanding solutions around the known class that’s not spherically symmetric but behaves similarly. More precisely, we prove that any given self-similarly expanding Goldreich-Weber star is codimension-4 stable in the class of irrotational perturbations. The codimension-4 condition is optimal and reflects the presence of 4 unstable directions of the linearised operator in self-similar coordinates, which are induced by the conservation of the energy and the momentum. This result can be viewed as the codimension-1 nonlinear stability of the “manifold” of self-similarly expanding GW-stars in the class of irrotational perturbations.
07 maart 2024 16:00 t/m 17:00
[PDE&A] Fred Wubs: Bifurcation Analysis of Fluid FlowsA better understanding of the mechanisms leading a fluid system to exhibit turbulent behavior is one of the grand challenges of the physical and mathematical sciences. Over the last few decades, numerical bifurcation methods have been extended and applied to a number of flow problems to identify critical conditions for fluid instabilities to occur. Together with Henk Dijkstra from IMAU, I taught a course in MasterMath which led to a book that provides a state-of-the-art account of these numerical methods. These methods also have a broad applicability in industrial, environmental and astrophysical flows.
In the presentation, I will discuss numerical methods for bifurcation analysis and show their application to some fluid flow problems.
More information on the book and accompanying software etc. can be found on
04 april 2024 16:00 t/m 17:00
[PDE&A] Matthew Thorpe: Linear Approximation and Manifold Learning in Optimal TransportOptimal transport distances are popular due to their 'modelling assumptions'. But significant drawbacks such as a lack of off-the-shelf data analysis tools and high computation cost limit their use in practice. The idea behind linear optimal transport is to define an embedding from an optimal transport space to a Euclidean space that approximates the topology. We start the talk by reviewing this embedding for the Wasserstein distance. Bounds on linear approximation are not particularly good if the full Wasserstein space is considered. To better control the approximation we consider a submanifold of the Wasserstein space and show one can get local linearisation of the same order as one expects for Riemannian manifolds in Euclidean spaces. We finally consider linearisation in the Hellinger--Kantorovich space, an extension of the Wasserstein distance to unbalanced measures. This is joint work with Tianji Cai, Junyi Cheng, Keaton Hamm, Caroline Moosemueller and Bernhard Schmitzer.
02 mei 2024 16:00 t/m 17:00