Mon, 20 Nov 2023
15:45
L5

OXPDE-WCMB seminar: From individual-based models to continuum descriptions: Modelling and analysis of interactions between different populations.

Mariya Ptashnyk
(Heriot-Watt University, Edinburgh)
Abstract

First we will show that the continuum counterpart of the discrete individual-based mechanical model that describes the dynamics of two contiguous cell populations is given by a free-boundary problem for the cell densities.  Then, in addition to interactions, we will consider the microscopic movement of cells and derive a fractional cross-diffusion system as the many-particle limit of a multi-species system of moderately interacting particles. 

Thu, 08 Feb 2018
15:00
L4

Non-existence and Non-uniqueness in the Kinetic Theory of Non-spherical Particles

Mark Wilkinson
(Heriot-Watt University, Edinburgh)
Abstract

The Boltzmann equation is a well-studied PDE that describes the statistical evolution of a dilute gas of spherical particles. However, much less is known — both from the physical and mathematical viewpoints — about the Boltzmann equation for non-spherical particles. In this talk, we present some new results on the non-existence and non-uniqueness of weak solutions to the initial-boundary value problem for N non-spherical particles which have importance for the Boltzmann equation.

We present work which was done jointly with L. Saint-Raymond (ENS Lyon), and also with P. Palffy-Muhoray (Kent State), E. Virga (Pavia) and X. Zheng (Kent State).

Fri, 27 Feb 2009
14:15
DH 1st floor SR

Multivariate utility maximization with proportional transaction costs

Mark Owen
(Heriot-Watt University, Edinburgh)
Abstract

My talk will be about optimal investment in Kabanov's model of currency exchange with transaction costs. The model is general enough to allow a random, discontinuous bid-offer spread. The investor wishes to maximize their "direct" utility of consumption, which is measured in terms of consumption assets linked to some (but not necessarily all) of the traded currencies. The analysis will centre on two conditions under which the existence of a dual minimiser leads to the existence of an optimal terminal wealth. The first condition is a well known, but rather unintuitive, condition on the utility function. The second weaker, and more natural condition is that of "asymptotic satiability" of the value function. We show that the portfolio optimization problem can be reformulated in terms of maximization of a terminal liquidation utility function, and that both problems have a common optimizer. This is joint work with Luciano Campi.

Mon, 15 Nov 2004
14:45
DH 3rd floor SR

On the inviscid limit for randomly forced nonlinear PDE

Professor Sergei Kuksin
(Heriot-Watt University, Edinburgh)
Abstract

I shall talk on recent results on behaviour of solutions of

2D Navier-Stokes Equation (and some other related equations), perturbed by a random force, proportional to the square root of the viscosity. I shall discuss some properties of the solutions, uniform in the viscosity, as well as the inviscid limit.

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