Related papers: Pseudo spectral collocation with Maxwell polynomia…
We investigate Maxwell-scalar models on radially symmetric spacetimes in which the gauge and scalar fields are coupled via the electric permittivity. We find the conditions that allow for the presence of minimum energy configurations. In…
Several classes of physical systems exhibit ultraslow diffusion for which the mean squared displacement at long times grows as a power of the logarithm of time ("strong anomaly") and share the interesting property that the probability…
This paper is concerned with diffusive approximations of peculiar numerical schemes for several linear (or weakly nonlinear) kinetic models which are motivated by wide-range applications, including radiative transfer or neutron transport,…
We develop a family of stabilized backward differentiation formula (sBDF) schemes of orders one through four for semilinear parabolic equations. The proposed methods are designed to achieve three properties that are rarely available…
We generalize our earlier results concerning meshfree collocation methods for semilinear elliptic second order problems to the quasilinear case. The stability question, however, is treated differently, namely by extending a paper on…
This paper aims to develop and analyze a numerical scheme for solving the backward problem of semilinear subdiffusion equations. We establish the existence, uniqueness, and conditional stability of the solution to the inverse problem by…
In this work, we propose a nonlinear stabilization technique for scalar conservation laws with implicit time stepping. The method relies on an artificial diffusion method, based on a graph-Laplacian operator. It is nonlinear, since it…
In this paper we introduce and discuss numerical schemes for the approximation of kinetic equations for flocking behavior with phase transitions that incorporate uncertain quantities. This class of schemes here considered make use of a…
Long global gyrokinetic turbulence simulations are particularly challenging in situations where the system deviates strongly from its initial state and when fluctuation level are high e.g. in strong gradient regions. For Particle-in-Cell…
We discuss the rigorous justification of the spatial discretization by means of Fourier spectral methods of quasilinear first-order hyperbolic systems. We provide uniform stability estimates that grant spectral convergence of the…
In this paper, we investigate the well-posedness of weak solutions to the time-fractional Fokker-Planck equation. Its dynamics is governed by anomalous diffusion, and we consider the most general case of space-time dependent forces.…
Maxwell equations describe the propagation of electromagnetic waves and are therefore fundamental to understanding many problems encountered in the study of antennas and electromagnetics. The aim of this paper is to propose and analyse an…
Maxwell-Stefan systems describing the dynamics of the molar concentrations of a gas mixture with an arbitrary number of components are analyzed in a bounded domain under isobaric, isothermal conditions. The systems consist of mass balance…
This paper presents a mathematical foundation for physical models in nonlinear optics through the lens of evolutionary equations. It focuses on two key concepts: well-posedness and exponential stability of Maxwell equations, with models…
Motivated by various applications, this article develops the notion of boundary control for Maxwell's equations in the frequency domain. Surface curl is shown to be the appropriate regularization in order for the optimal control problem to…
This review is a kinetic theory study investigating the effects of inelasticity on the structure of the non-equilibrium states, in particular on the behavior of the velocity distribution in the high energy tails. Starting point is the…
We present a low order virtual element discretization for time dependent Maxwell's equations, which allow for the use of general polyhedral meshes. Both the semi- and fully-discrete schemes are considered. We derive optimal a priori…
In this paper we consider unconditionally energy stable numerical schemes for the nonstationary 3D magneto-micropolar equations that describes the microstructure of rigid microelements in electrically conducting fluid flow under some…
Wave propagation problems have many applications in physics and engineering, and the stochastic effects are important in accurately modeling them due to the uncertainty of the media. This paper considers and analyzes a fully discrete finite…
We propose a collocation method based on multivariate polynomial splines over triangulation or tetrahedralization for the numerical solution of partial differential equations. We start with a detailed explanation of the method for the…