相关论文: On existence of spatially regular strong solutions…
The paper considers a class of linear Boltzmann transport equations which models a charged particle transport. The equation is an approximation of the original exact transport equation which involves hyper-singular integrals in their…
We show existence of a regular solution in Sobolev-Slobodetskii spaces to stationary transport equation with inflow boundary condition in a bounded domain $\Omega \subset \mathbb{R}^2$. Our result is subject to quite general constraint on…
The aim of the paper is to develop a general theory of solvability of linear inhomogeneous boundary-value problems for systems of ordinary differential equations of arbitrary order in Sobolev spaces. Boundary conditions are allowed to be…
We prove existence and uniqueness of solutions to the initial-boundary value problem for the Lifshitz--Slyozov equation (a nonlinear transport equation on the half-line), focusing on the case of kinetic rates with unbounded derivative at…
We establish existence and uniqueness results for initial-boundary value problems for transport equations in one space dimension with nearly incompressible velocity fields, under the sole assumption that the fields are bounded. In the case…
The initial-boundary value problems for linear non-autonomous first order evolution equations are examined. Our assumptions provide a unified treatment which is applicable to many situations, where the domains of the operators may change…
We consider the most general class of linear inhomogeneous boundary-value problems for systems of ordinary differential equations of an arbitrary order whose solutions and right-hand sides belong to appropriate Sobolev spaces. For…
This paper is concerned with the initial-boundary value problem \; for stochastic transport equations in bounded domains. For a given stochastic perturbation of the drift vector field, we prove existence and uniqueness of weak solutions…
We prove some sharp regularity results for solutions of classical first order hyperbolic initial boundary value problems. Our two main improvements on the existing litterature are weaker regularity assumptions for the boundary data and…
This paper proves the existence of small-amplitude global-in-time unique mild solutions to both the Landau equation including the Coulomb potential and the Boltzmann equation without angular cutoff. Since the well-known works (Guo, 2002)…
In this article we investigate the spatial Sobolev regularity of mild solutions to stochastic Burgers equations with additive trace class noise. Our findings are based on a combination of suitable bootstrap-type arguments and a detailed…
We consider the regularity of stationary solutions to the linearized Boltzmann equations in bounded $C^1$ convex domains in $\mathbb{R}^3$ for gases with cutoff hard potential and cutoff Maxwellian gases. We prove that the stationary…
We study steady solutions to the relativistic Boltzmann equation with hard-sphere interactions in a slab geometry. Under a spatial symmetry assumption in the transverse variables $x_2$ and $x_3$, the problem reduces to a one-dimensional…
We show the existence of strong solutions in Sobolev-Slobodetskii spaces to the stationary compressible Navier-Stokes equations with inflow boundary condition. Our result holds provided certain condition on the shape of the boundary around…
We consider the stationary Boltzmann equation with the angular cutoff cross section in a bounded convex domain under the incoming boundary condition. In this article, we discuss the fractional Sobolev regularity of the solution without…
The paper considers existence results of solution for a linear coupled system of Boltzmann transport equations and related inverse problem. The system models the evolution of three species of particles, photons, electrons and positrons.…
We consider an inhomogeneous initial-boundary value problem for a Petrovskii parabolic system of second order PDEs. We prove that this problem induces isomorphisms between appropriate anisotropic generalized Sobolev spaces. The regularity…
This paper considers the neutron transport equation in bounded domain with a combination of the diffusive boundary condition and the in-flow boundary condition. We firstly study the existence of solution in any fixed time by…
Initial-boundary value problems in a half-strip with different types of boundary conditions for two-dimensional Zakharov-Kuznetsov equation are considered. Results on global well-posedness in classes of regular solutions in the cases of…
We study linear and quasilinear Venttsel boundary value problems involving elliptic operators with discontinuous coefficients. On the base of the a priori estimates obtained, maximal regularity and strong solvability in Sobolev spaces are…