Related papers: Self-similarity and diffusive limits for linear ki…
In this work we present new exact similarity solutions with moving boundaries of the Fokker-Planck equation having both time-dependent drift and diffusion coefficients.
We study linear inhomogeneous kinetic equations with an external confining potential and a collision operator admitting several local conservation laws (local density, momentum and energy). We classify all special macroscopic modes…
We obtain the existence, uniqueness and regularity results for solutions to kinetic Fokker-Planck equations with bounded measurable coefficients in the presence of boundary conditions, including the inflow, diffuse reflection and specular…
We propose a unified method for the large space-time scaling limit of \emph{linear} collisional kinetic equations in the whole space. The limit is of \emph{fractional} diffusion type for heavy tail equilibria with slow enough decay, and of…
The present work deals with the two-dimensional incompressible,laminar, steady-state boundary layer equations. First, we determinea family of velocity distributions outside the boundary layer suchthat these problems may have similarity…
We address a general system of nonlinear Dirac equations in (1+1) dimensions and prove nonexistence of classical self-similar blowup solutions in the space of bounded functions. While this argument does not exclude the possibility of…
This paper deals with the two-dimensional incompressible, laminar, steady-state boundary layer equations.First, we determine a family of velocity distributions outside the boundary layer such that these problems may have similarity…
Perfect fluid spacetimes admitting a kinematic self-similarity of infinite type are investigated. In the case of plane, spherically or hyperbolically symmetric space-times the field equations reduce to a system of autonomous ordinary…
This paper focuses on the long-term behavior of solutions to nonlinear stochastic Fokker-Planck equations driven by common noise, where the drift term has a linear dependence on the measure. These equations, which describe the evolution of…
Self-similarity in general relativity is briefly reviewed and the differences between self-similarity of the first kind and generalized self-similarity are discussed. The covariant notion of a kinematic self-similarity in the context of…
We study the long-time behavior of localized solutions to linear or semilinear parabolic equations in the whole space $\mathbb{R}^n$, where $n \ge 2$, assuming that the diffusion matrix depends on the space variable $x$ and has a finite…
We consider a particle living in $\mathbb{R}_+$, whose velocity is a positive recurrent diffusion with heavy-tailed invariant distribution when the particle lives in $(0,\infty)$. When it hits the boundary $x=0$, the particle restarts with…
In this paper, we propose a general framework to design asymptotic preserving schemes for the Boltzmann kinetic kinetic and related equations. Numerically solving these equations are challenging due to the nonlinear stiff collision (source)…
General self-consistent expressions for the coefficients of diffusion and dynamical friction in a stable, bound, multicomponent self-gravitating and inhomogeneous system are derived. They account for the detailed dynamics of the colliding…
We study models kinetic models of polymeric fluids. We introduce a notion of solutions which is based on moments of polymeric distributions. We prove global existence and uniqueness of a large class of initial data for diffusive systems of…
We study long time behavior of some nonlinear discrete velocity kinetic equations in the one and three dimensions with periodic boundary conditions. We prove the exponential time decay of solutions towards the global equilibrium in the…
We present a unified approach to characterising fast-reaction limits of systems of either two reaction-diffusion equations, or one reaction-diffusion equation and one ordinary differential equation, on unbounded domains, motivated by models…
We prove global stability results of {\sl DiPerna-Lions} renormalized solutions for the initial boundary value problem associated to some kinetic equations, from which existence results classically follow. The (possibly nonlinear) boundary…
The Vlasov-Nordstr\"{o}m-Fokker-Planck system describes the evolution of self-gravitating matter experiencing collisions with a fixed background of particles in the framework of a relativistic scalar theory of gravitation. We study the…
Kinetics of collision processes with linear mixing rules are investigated analytically. The velocity distribution becomes self-similar in the long time limit and the similarity functions have algebraic or stretched exponential tails. The…