The Asymptotics of the Heat Equation for a Boundary Value Problem.
The Boubaker polynomials expansion scheme BPES for solving a standard boundary value problem.
The cost of controlling unstable systems: time irreversible systems.
The Dirichlet problem in weighted spaces on a dihedral domain
We examine the Dirichlet problem for the Poisson equation and the heat equation in weighted spaces of Kondrat'ev's type on a dihedral domain. The weight is a power of the distance from a distinguished axis and it depends on the order of the derivative. We also prove a priori estimates.
The distribution of energy in the Brownian motion in the Gaussian field and analytic-hypoellipticity of certain subelliptic operators on the Heisenberg group
The dynamics of a levitated cylindrical permanent magnet above a superconductor.
When a permanent magnet is released above a superconductor, it is levitated. This is due to the Meissner-effect, i.e. the repulsion of external magnetic fields within the superconductor. In experiments, an interesting behavior of the levitated magnet can be observed: it might start to oscillate with increasing amplitude and some magnets even reach a continuous rotation. In this paper we develop a mathematical model for this effect and identify by analytical methods as well with finite element simulations...
The evolution of harmonic maps
The functional calculus for the laplacian on Lipschitz domains
The Geometry of Differential Harnack Estimates
In this short note, we hope to give a rapid induction for non-experts into the world of Differential Harnack inequalities, which have been so influential in geometric analysis and probability theory over the past few decades. At the coarsest level, these are often mysterious-looking inequalities that hold for ‘positive’ solutions of some parabolic PDE, and can be verified quickly by grinding out a computation and applying a maximum principle. In this note we emphasise the geometry behind the Harnack...
The heat equation and harmonic maps of complete manifolds.
The heat equation in riemannian geometry
The heat flows and harmonic maps of complete noncompact Riemannian manifolds.
The heat kernel on Lie groups.
The Neumann problem for the heat equation in non-cylindrical domains
I shall discuss joint work with John L. Lewis on the solvability of boundary value problems for the heat equation in non-cylindrical (i.e., time-varying) domains, whose boundaries are in some sense minimally smooth in both space and time. The emphasis will be on the Neumann problem with data in . A somewhat surprising feature of our results is that, in contrast to the cylindrical case, the optimal results hold when , with the situation getting progressively worse as approaches . In particular,...
The Numerical Solution of the Inverse Stefan Problem.
The quasi-stationary approximation for the Stefan problem with a convective boundary condition.
The Residue of the Local Eta Function at the Origin.
The solution of an axially symmetric boundary value problem of the generalized heat equation and its application in the technology of microschemes
The spread of the potential on a weighted graph.
The temperature of an asteroid