Smoothing properties in multistep backward difference method and time derivative approximation for linear parabolic equations.
Solitary-wave propagation and interactions for a sixth-order generalized Boussinesq equation.
Solutions for the cell cycle in cell lines derived from human tumors.
Solutions to Maxwell equations for an electromagnetic beam injected into a plasma.
Some applications of parabolic differential equations of Allen-Cahn type in image processing
Some new results in multiphase geometrical optics
Some new results in multiphase geometrical optics
In order to accommodate solutions with multiple phases, corresponding to crossing rays, we formulate geometrical optics for the scalar wave equation as a kinetic transport equation set in phase space. If the maximum number of phases is finite and known a priori we can recover the exact multiphase solution from an associated system of moment equations, closed by an assumption on the form of the density function in the kinetic equation. We consider two different closure assumptions based on delta...
Some remarks concerning stabilization techniques for convection--diffusion problems
There are many methods and approaches to solving convection--diffusion problems. For those who want to solve such problems the situation is very confusing and it is very difficult to choose the right method. The aim of this short overview is to provide basic guidelines and to mention the common features of different methods. We place particular emphasis on the concept of linear and non-linear stabilization and its implementation within different approaches.
Some tracks in air pollution modelling and simulation.
In this article we discuss some issues related to Air Pollution modelling (as viewed by the authors): subgrid parametrization, multiphase modelling, reduction of high dimensional models and data assimilation. Numerical applications are given with POLAIR, a 3D numerical platform devoted to modelling of atmospheric trace species.
Source terms identification for time fractional diffusion equation.
Stabile Mehrschichtverfahren für parabolische Evolutionsgleichungen.
Stability and consistency of the semi-implicit co-volume scheme for regularized mean curvature flow equation in level set formulation
We show stability and consistency of the linear semi-implicit complementary volume numerical scheme for solving the regularized, in the sense of Evans and Spruck, mean curvature flow equation in the level set formulation. The numerical method is based on the finite volume methodology using the so-called complementary volumes to a finite element triangulation. The scheme gives the solution in an efficient and unconditionally stable way.
Stability and Convergence of the Difference Schemes for Equations of Isentropic Gas Dynamics in Lagrangian Coordinates
Stability criteria for a class of discrete reaction-diffusion equations.
Stability of a family of multi-time-level difference schemes for the advection equation.
Stability of a second order of accuracy difference scheme for hyperbolic equation in a Hilbert space.
Stability of discrete shocks for difference approximations to systems of conservation laws.
Stability of finite difference schemes for certain problems in biology
We consider a generalized 1-D von Foerster equation. We present two discretization methods for the initial value problem and study stability of finite difference schemes on regular meshes.
Stability of solutions of differential-operator and operator-difference equations with respect to perturbation of operators
Study of convergence of the projection-difference method for hyperbolic equations.