We establish the convergence to equilibrium for various linear collisional kinetic equations (including linearized Boltzmann and Landau equations) with physical local conservation laws in bounded domains general Maxwell boundary condition. Our proof consists establishing an hypocoercivity result associated operator, other words, we exhibit a convenient Hilbert norm which operator is coercive or...

This paper deals with convergence theorems of the Galerkin finite element approximation for second-order elliptic boundary value problems. Under some quite general settings, we show not only pointwise but also prove that norm approximate operator converges to corresponding inverse a linear operator. Since estimates linearized play an essential role in numerical verification method solutions non...

We establish the conditional asymptotic stability in a local energy norm of unstable soliton for one-dimensional quadratic Klein-Gordon equation under even perturbations. A key feature problem is positive gap eigenvalue exhibited by linearized operator around soliton. Our proof based on several virial-type estimates, combining techniques from series works [23], [24], [25], [27], [28], and an ex...

The linearized collision operator of the Boltzmann equation can in a natural way be written as sum positive multiplication operator, frequency, and an integral operator. Compactness for monatomic single species is classical result, while corresponding result mixtures more recently obtained. In this work compactness polyatomic species, where polyatomicity modeled by discrete internal energy vari...

For linearized Navier–Stokes equations, we consider an inverse source problem of determining a spatially varying divergence-free factor. We prove the global Lipschitz stability by interior data over time interval and velocity field at t0>0 spatial domain. The key machinery are Carleman estimates for equations operator rot.

The alternating direction method of multipliers (ADMM) is being widely used for various convex minimization models with separable structures arising in a variety of areas. In the literature, the proximal version of ADMM which allows ADMM’s subproblems to be proximally regularized has been well studied. Particularly the linearized version of ADMM can be yielded when the proximal terms are approp...

The paper investigates waves generated by the moving loads on ice plates floating an incompressible fluid. Two different viscoelastic approximations are considered for cover: A model depending strain-relaxation time, and a including hereditary delay integral. problem is formulated in terms of exact dispersion relation Dirichlet–Neumann operator connected to fluid motion. Weakly nonlinear linear...

We show that the widely used relaxation time approximation to relativistic Boltzmann equation contains basic flaws, being incompatible with microscopic and macroscopic conservation laws. propose a new fixes such fundamental issues maintains properties of linearized collision operator. how this correction affects transport coefficients, as bulk viscosity particle diffusion.

Recently a linearized perturbation theory has been formulated for soliton sectors of quantum field theories. While it is more economical than alternative formalisms, such as collective coordinates, currently limited to solitons which stay close base point, about the linearized. As result, so far this formalism only applied stationary solitons. In spite limitation, we construct kink states with ...