On the global solvability of solutions to a quasilinear wave equation with localized damping and source terms.
On the interior boundary-value problem for the stationary Povzner equation with hard and soft interactions
The Povzner equation is a version of the nonlinear Boltzmann equation, in which the collision operator is mollified in the space variable. The existence of stationary solutions in is established for a class of stationary boundary-value problems in bounded domains with smooth boundaries, without convexity assumptions. The results are obtained for a general type of collision kernels with angular cutoff. Boundary conditions of the diffuse reflection type, as well as the given incoming profile, are...
On the Landau approximation in plasma physics
On the order of pointwise convergence of some boundary element methods. Part I. Operators of negative and zero order
On the spectrum of orthomorphisms and Barbashin operators.
On the stationary solutions of Burgers' equation
On the strong convergence to equilibrium of the Foiaş solutions of the transport equation
We define the Foiaş solutions of the transport equation and we prove that the strong asymptotic stability of the Foiaş solutions is equivalent to the asymptotic stability of the solutions of the transport equation in L¹.
On the Tjon-Wu representation of the Boltzmann equation
On the unique solvability of a nonlocal phase separation problem for multicomponent systems
A nonlocal model of phase separation in multicomponent systems is presented. It is derived from conservation principles and minimization of free energy containing a nonlocal part due to particle interaction. In contrast to the classical Cahn-Hilliard theory with higher order terms this leads to an evolution system of second order parabolic equations for the particle densities, coupled by nonlinear and nonlocal drift terms, and state equations which involve both chemical and interaction potential...
On the wave equations with memory in noncylindrical domains.
On three problems of neutron transport theory
In this paper, the initial-value problem, the problem of asymptotic time behaviour of its solution and the problem of criticality are studied in the case of linear Boltzmann equation for both finite and infinite media. Space of functions where these problems are solved is chosen in such a vay that the range of physical situations considered may be so wide as possible. As mathematical apparatus the theory of positive bounded operators and of semigroups are applied. Main results are summarized in...
On weak solutions to a viscoelasticity model
One-dimensional model describing the non-linear viscoelastic response of materials
In this paper we consider a model of a one-dimensional body where strain depends on the history of stress. We show local existence for large data and global existence for small data of classical solutions and convergence of the displacement, strain and stress to zero for time going to infinity.
Optimal control approach in inverse radiative transfer problems : the problem on boundary function
Optimal control approach in inverse radiative transfer problems: the problem on boundary function
The paper presents some results related to the optimal control approachs applying to inverse radiative transfer problems, to the theory of reflection operators, to the solvability of the inverse problems on boundary function and to algorithms for solution of these problems.
Optimization of weighted Monte Carlo methods with respect to auxiliary variables.
Particle simulation and asymptotic analysis of kinetic equations for modeling a Schottky diode
Pattern and Waves for a Model in Population Dynamics with Nonlocal Consumption of Resources
We study a reaction-diffusion equation with an integral term describing nonlocal consumption of resources in population dynamics. We show that a homogeneous equilibrium can lose its stability resulting in appearance of stationary spatial structures. They can be related to the emergence of biological species due to the intra-specific competition and random mutations. Various types of travelling waves are observed.
Point Approximation of a Space-Homogeneous Transport Equation.
Pointwise convergence of some boundary element methods. Part II