Nonlinear differential systems of the third and fourth order
This survey paper presents lecture notes from a series of four lectures addressed to a wide audience and it offers an introduction to several topics in conformal differential geometry. In particular, a very nice and gentle introduction to the conformal Riemannian structures themselves, flat or curved, is presented in the beginning. Then the behavior of the covariant derivatives under the rescaling of the metrics is described. This leads to Penrose’s local twistor transport which is introduced in...
We consider a contact problem of planar elastic bodies. We adopt Coulomb friction as (an implicitly defined) constitutive law. We will investigate highly simplified lumped parameter models where the contact boundary consists of just one point. In particular, we consider the relevant static and dynamic problems. We are interested in numerical solution of both problems. Even though the static and dynamic problems are qualitatively different, they can be solved by similar piecewise-smooth continuation...
We solve the one-dimensional stochastic heat equation driven by fractional Brownian motion using the modified Euler-Maruyama finite differences method. We use the numerical solution as our observation and we show how to estimate the drift parameter from a one path only.
We study a numerical method for the diffusion of an age-structured population in a spatial environment. We extend the method proposed in [2] for linear diffusion problem, to the nonlinear case, where the diffusion coefficients depend on the total population. We integrate separately the age and time variables by finite differences and we discretize the space variable by finite elements. We provide stability and convergence results and we illustrate our approach with some numerical result.