Related papers: Global Existence for the Vlasov-Poisson System in …
We consider a modified version of the Vlasov-Maxwell system in which the usual Maxwell fields are replaced by their retarded parts. We show that solutions of this modified system exist globally for a small number of particles and that they…
The aim of this article is to prove an "almost" global existence result for some semilinear wave equations in the plane outside a bounded convex obstacle with the Neumann boundary condition.
In this work we prove global existence and uniform boundedness of solutions of 2X2 reaction-diffusion systems with control of mass structure and nonlinearities of unlimited growth. Furthermore the results are obtained without restrictions…
The Vlasov-Poisson-Boltzmann equation is a classical equation governing the dynamics of charged particles with the electric force being self-imposed. We consider the system in a convex domain with the Cercignani-Lampis boundary condition.…
We consider the Boltzmann equation with external fields in strictly convex domains with diffuse reflection boundary condition. As long as the normal derivative of external fields satisfy some sign condition on the boundary (1.8) we…
We prove global existence of solutions to the Cauchy problem for the compressible Navier-Stokes equations in Euclidean spaces, given initial data with small norms in Besov and critical weighted Besov spaces. Global existence and a priori…
We consider the Vlasov--Poisson system in a $C^3$ convex domain $D$ with a perfectly conducting wall. We introduce the asymptotic domain $D_{\infty}$ for the domain $D$. Then under acceptable assumptions on $D$, we show that for localized…
We study the Lagrangian structure of relativistic Vlasov systems, such as the relativistic Vlasov-Poisson and the relativistic quasi-eletrostatic limit of Vlasov-Maxwell equations. We show that renormalized solutions of these systems are…
We establish the global-wellposedness and stability of the Boltzmann equation with the specular reflection boundary condition in general smooth convex domains when an initial datum is close to the Maxwellian with or without a small external…
We consider the Vlasov-Poisson system with initial data a small, radial, absolutely continuous perturbation of a point charge. We show that the solution is global and disperses to infinity via a modified scattering along trajectories of the…
We show the direct applicability of the Brouwer fixed point theorem for the existence of equilibrium points and periodic solutions for differential systems on general domains satisfying geometric conditions at the boundary. We develop a…
This paper has been withdrawn by the authors. We consider the attraction-repulsion chemotaxis system (3 complicated PDEs system) under homogeneous Neumann boundary conditions in a bounded domain {\Omega} with smooth boundary, then the…
We study well-posedness and long time behavior of the nonlinear Vlasov-Poisson- Fokker-Planck system with an external confining potential. The system describes the time evolution of particles (e.g.$\,\,$in a plasma) undergoing diffusion,…
We prove the existence of axially symmetric solutions to the Vlasov--Poisson system in a rotating setting for sufficiently small angular velocity. The constructed steady states depend on Jacobi's integral and the proof relies on an implicit…
We consider the two-dimensional Vlasov-Poisson system to model a two-component plasma whose distribution function is constant with respect to the third space dimension. First, we show how this two-dimensional Vlasov-Poisson system can be…
The Cauchy problem is revisited for the so-called relativistic Vlasov-Poisson system in the attractive case. Global existence and uniqueness of spherical classical solutions is proved under weaker assumptions than previously used. A new…
This paper aims to prove the global existence of solutions for coupled reaction diffusion equations with a balance Law and nonlinearities with a non constant sign. The case when one (or both) of the components of the solution is not a…
In the paper, we prove the existence of radial solutions to \begin{equation}\notag%\label{main-eq-abstarct} %\begin{aligned} -\Delta_p u+({\rm sgn}(p-s)+V(x))|u|^{p-2}u+\lambda |u|^{s-2}u=|u|^{q-2}u\qquad\text{in}\,\R^N \\…
We prove an existence theorem for convex hypersurfaces of prescribed Gauss curvature in the complement of a compact set in Euclidean space which are close to a cone.
We prove in the cases of plane and hyperbolic symmetries a global in time existence result in the future for comological solutions of the Einstein-Vlasov-scalar field system, with the sources generated by a distribution function and a…