相关论文: The Landau equation with the specular reflection b…
The present article proposes a rigorous derivation of the Boltzmann equation in the half-space. We show an analog of the Lanford's theorem in this domain, with specular reflection boundary condition, stating the convergence in the low…
We establish Lipschitz stability for both the potential and the initial conditions from a single boundary measurement in the context of a hyperbolic boundary initial value problem. In our setting, the initial conditions are allowed to…
We prove the uniqueness of weak solutions to the spatially homogeneous special relativistic Landau equation under the conditional assumption that the solution satisfies $(p^0)^7 F(t,p) \in L^1 ([0,T]; L^\infty)$. The existence of standard…
We consider the initial boundary value problem of Landau-Lifshitz-Bloch equation on three-dimensional ferromagnetic films, where the effective field contains the stray field controlled by Maxwell equation and the exchange field contains…
We investigate the stability and long-term behavior of spatially periodic plane waves in the complex Klein-Gordon equation under localized perturbations. Such perturbations render the wave neither localized nor periodic, placing its…
We establish that solitary stationary waves in three dimensional viscous incompressible fluids are a generic phenomenon and that every such solution is a vanishing wave-speed limit along a one parameter family of traveling waves. The…
We investigate the diffusive Hamilton-Jacobi equation $$u_t-\Lap u = |\nabla u|^p$$ with $p>1$, in a smooth bounded domain of $\RN$ with homogeneous Neumann boundary conditions and $W^{1,\infty}$ initial data. We show that all solutions…
The initial-boundary value problem in a bounded domain with moving boundaries and nonhomogeneous boundary conditions for a higher order nonlinear Schr\"odinger (HNLS) equation is considered. Existence and uniqueness of global weak solutions…
The equation arising from Prandtl boundary layer theory is considered. The existence of the entropy solution can be proved by BV estimate method. The interesting problem is that, since a may be degenerate on the boundary, the usual boundary…
This paper investigates the Cauchy problem of the spatially homogeneous Landau equation with soft potential under the perturbation framework to global equilibrium. We prove that the solution to the Cauchy problem exhibits analyticity in the…
This paper is concerned with the boundary-value problem on the Boltzmann equation in bounded domains with diffuse-reflection boundary where the boundary temperature is time-periodic. We establish the existence of time-periodic solutions…
We provide a formulation of the initial boundary value problem for Friedrich's extended conformal Einstein field equations in which boundary data is prescribed on a timelike hypersurface located at a finite position in the spacetime. Our…
This article studies a Fokker-Planck type equation of fractional diffusion with conservative drift $\partial$f/$\partial$t = $\Delta$^($\alpha$/2) f + div(Ef), where $\Delta$^($\alpha$/2) denotes the fractional Laplacian and E is a…
We consider driftless stochastic differential equations and the diffusions starting from the positive half line. It is shown that the Feller test for explosions gives a necessary and sufficient condition to hold pathwise uniqueness for…
This paper deals with the homogeneous Neumann boundary-value problem for the chemotaxis-consumption system \begin{eqnarray*} \begin{array}{llc} u_t=\Delta u-\chi\nabla\cdot (u\nabla v)+\kappa u-\mu u^2,\\ v_t=\Delta v-uv, \end{array}…
We study Maxwell's equations in conducting media with perfectly conducting boundary conditions on Lipschitz domains, allowing rough material coefficients and $L^2$-data. Our first contribution is a direct proof of well-posedness of the…
The Lenard-Balescu equation was formally derived in the 1960s as the fundamental description of the collisional process in a spatially homogeneous system of interacting particles. It can be viewed as correcting the standard Landau equation…
In this work, we deal with the Vlasov-Poisson system in smooth physical domains with specular boundary condition, under mild integrability assumptions, and $d \ge 3$. We show that the Lagrangian and Eulerian descriptions of the system are…
The problem of diamagnetism, solved by Landau, continues to pose fascinating issues which have relevance even today. These issues relate to inherent quantum nature of the problem, the role of boundary and dissipation, the meaning of…
In this manuscript we consider an isotropic modification for the Landau equation with Coulomb potential in three space dimensions. Global in time existence of weak solutions for even initial data is shown by employing a time…