We consider an initial-value problem based on a class of scalar nonlinear hyperbolic reaction–diffusion equations of the general form $$begin{align*} & u_{tautau}+u_{tau}=u_{{xx}}+varepsilon (F(u)+F(u)_{tau} ), end{align*}$$ in which ${x}…
We study SDE and PDE models for opinion dynamics under bounded confidence, for a range of different boundary conditions, with and without the inclusion of a radical population. We perform exhaustive numerical studies with pseudo-spectral methods to det…
In this paper, we constructed a family of steady vortex solutions for the lake equations with a general vorticity function, which constitutes a desingularization of a singular vortex. The precise localization of the asymptotic singular vortex is shown …
We study the spectrum of the Laplace–Beltrami operator on ellipsoids. For ellipsoids that are close to the sphere, we use analytic perturbation theory to estimate the eigenvalues up to two orders. We show that for biaxial ellipsoids sufficiently…
Point vortex systems that include vortices with constant coordinate functions are largely unexplored, even though they have reasonable physical interpretations in the geophysical context. Here, we investigate the dynamical aspects of the restricted thr…