6 problems

Fractional differential equation systems may be nonlinear and non-autonomous, and an inertial manifold is a reduced finite-dimensional manifold intended to capture their long-time…

Let $\Omega=(0,1)\times\widehat{\Omega}$, where $\widehat{\Omega}\subseteq\mathbb{R}^{d-1}$ is open and bounded, and let $\alpha\in L_\infty(0,1)$ be piecewise constant. For…

Let the heterogeneous diffusivity be random and non-periodic, and compare a computational homogenisation prediction obtained from a single realisation with one obtained from an ens…

Let $\widehat \sigma_1^*$ denote the supremum of the first nonzero Steklov eigenvalue multiplied by the boundary length, over planar domains of area $\pi$, and let…

Let $L(t)$ denote the limiting family of linear operators arising in the scaling limit where the quantum wavelength and scattering radius satisfy $h=r\to0$, with observables evolve…

Scaling conjecture. In the case $0<\alpha<2$, the correct scaling for obtaining a non-trivial homogenisation limit is