The relativistic Boltzmann equation for a constant differential cross section and with periodic boundary conditions is considered. The speed of light appears as a parameter c>c0 for a properly large and positive c0. A local existence and uniqueness theorem is proved in an interval of time independent of c>c0 and conditions are given such that in the limit c→+∞ the solutions converge, in a suita...

We will mainly consider the Sinh-Gordon model in finite spacial volume which corresponds to imposing the periodic boundary conditions φ(x + R) = φ(x). A lot is known about the Sinh-Gordon model in infinite volume R → ∞, see e.g. [1, 2, 3, 4, 5]. The spectrum contains a single particle with mass m which is related to the parameter μ in (1.1) in a definite way [6], see eqn. (5.32) below. The S-ma...

We consider parameter-elliptic boundary value problems and uniform a priori estimates in Lp-Sobolev spaces of Bessel potential and Besov type. The problems considered are systems of uniform order and mixed-order systems (Douglis-Nirenberg systems). It is shown that compatibility conditions on the data are necessary for such estimates to hold. In particular, we consider the realization of the bo...

We present a modular toolbox for parallel nite element simulations on distributed memory systems. The library named PadFEM includes a graphical editor for specifying domains with boundary conditions, automatic mesh generation, automaticmesh partitioning and mapping onto the processors of a MIMD-system. The parallel FEM-simulation uses the preconditioned conjugate gradient method. The paralleliz...

In this paper, we study a second order differential operator with mixed nonlocal boundary conditions combined weighting integral boundary condition with another two point boundary condition. Under certain conditions on the weighting functions and on the coefficients in the boundary conditions, called non regular boundary conditions, we prove that the resolvent decreases with respect to the spec...

This work is aimed at the derivation of reliable and efficient a posteriori error estimates for convectiondominated diffusion problems motivated by a linear Fokker-Planck problem appearing in computational neuroscience. We obtain computable error bounds of functional type for the static and time-dependent case and for different boundary conditions (mixed and pure Neumann boundary conditions). F...

Maxwell equations are posed as variational boundary value problems in the function space H(curl) and are discretized by Nédélec finite elements. In Beck et al., 2000, a residual type a posteriori error estimator was proposed and analyzed under certain conditions onto the domain. In the present paper, we prove the reliability of that error estimator on Lipschitz domains. The key is to establish ...

Abstract. We consider a Korteweg-de Vries equation perturbed by a noise term on a bounded interval with periodic boundary conditions. The noise is additive, white in time and “almost white in space”. We get a local existence and uniqueness result for the solutions of this equation. In order to obtain the result, we use the precise regularity of the Brownian motion in Besov spaces, and the metho...

When the permeability field of a given porous medium domain is heterogeneous by the existence of randomly distributed fractures such that numerical investigation becomes cumbersome, another level of upscaling may be required. That is such complex permeability field could be relaxed i.e., smoothed by constructing an effective permeability field. The effective permeability field is an approximati...

We consider a finite string where, at both end points, a homogeneous Dirichlet boundary condition holds. One boundary point is fixed, and the other is moving; hence the length of the string is changing in time. The string is controlled through the movement of this boundary point. We consider movements of the boundary that are Lipschitz continuous. Only movements for which at the given finite te...