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...

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...

We are interested in the homogenization of energy like quantities for electromagnetic waves in the high frequency limit for Maxwell's equations with various boundary conditions. We use a scaled variant of H-measures known as semi classical measures or Wigner measures. Firstly, we consider this system in the half space of R 3 in the time harmonic and with conductor boundary condition at the flat...

Convergence properties of additive and multiplicative Schwarz iterations for solving linear systems of equations with a symmetric positive semidefinite matrix are analyzed. The analysis presented applies to matrices whose principal submatrices are nonsingular, i.e., positive definite. These matrices appear in discretizations of some elliptic partial differential equations, e.g., those with Neum...

In this paper, we deal with controllability properties of linear and nonlinear Korteweg–de Vries equations in a bounded interval. The main part of this paper is a result of uniform controllability of a linear KdV equation in the limit of zero-dispersion. Moreover, we establish a result of null controllability for the linear equation via the left Dirichlet boundary condition, and of exact contro...