相关论文: Boundedness estimates for nonlinear nonlocal kinet…

We study the regularity of weak solutions to nonlocal in time subdiffusion equations for a wide class of weakly singular kernels appearing in the generalised fractional derivative operator. We prove a weak Harnack inequality for nonnegative…

We study the long-time behaviour of a nonlinear Fokker-Planck equation, which models the evolution of rigid polymers in a given flow, after a closure approximation. The aim of this work is twofold: first, we propose a microscopic derivation…

The existence and uniqueness of measure-valued solutions to stochastic nonlinear, non-local Fokker-Planck equations is proven. This type of stochastic PDE is shown to arise in the mean field limit of weakly interacting diffusions with…

We prove local boundedness, Harnack's inequality and local regularity for weak solutions of quasilinear degenerate elliptic equations in divergence form with Rough coefficients. Degeneracy is encoded by a non-negative, symmetric, measurable…

We show that degenerate nonlinear diffusion equations can be asymptotically obtained as a limit from a class of nonlocal partial differential equations. The nonlocal equations are obtained as gradient flows of interaction-like energies…

We extend the De Giorgi--Nash--Moser theory to a class of kinetic Fokker-Planck equations and deduce new results on the Landau-Coulomb equation. More precisely, we first study the H{\"o}lder regularity and establish a Harnack inequality for…

The aim of this work is to prove a Harnack inequality and the H\"older continuity for weak solutions to the Kolmogorov equation $\mathscr{L} u = f$ with measurable coefficients, integrable lower order terms and nonzero source term. We…

In this paper, we study the nonlinear Vlasov-Fokker-Planck equation with fixed collision frequency. We establish the global-in-time existence of weak solutions to the equation with large initial data. Moreover, we show that our solution…

We consider linear and obstacle problems driven by a nonlocal integral operator, for which nonlocal interactions are restricted to a ball of finite radius. These type of operators are used to model anomalous diffusion and, for a special…

We consider kinetic Fokker-Planck (or Vlasov-Fokker-Planck) equations on the torus with Maxwellian or fat tail local equilibria. Results based on weak norms have recently been achieved by S. Armstrong and J.-C. Mourrat in case of Maxwellian…

In this paper, we investigate the incompressible Navier-Stokes equations coupled with the Vlasov-Fokker-Planck equation, which describes a two-phase mixture of the viscous incompressible fluid with particles or bubbles through a frictional…

We study the boundary regularity of local weak solutions to nonlinear parabolic systems of the form \begin{equation*} \partial_t u^i - \mathrm{div} \big( a(|Du|) Du^i \big)= f^i, \qquad i=1,\dots,N, \end{equation*} in a space-time cylinder…

This paper focuses on the study of semilinear fractional diffusion-wave equations in the context of critical nonlinearities. Firstly, we address the issue of local well-posedness for the problem, examine spatial regularity, and the…

We obtain equilibration rates for a one-dimensional nonlocal Fokker-Planck equation with time-dependent diffusion coefficient and drift, modeling the relaxation of a large swarm of robots, feeling each other in terms of their distance,…

In this paper we investigate the stationary profiles of a nonlinear Fokker-Planck equation with small diffusion and nonlinear in- and outflow boundary conditions. We consider corridors with a bottleneck whose width has a global…

We investigate the fractional diffusion approximation of a kinetic equation in the upper-half plane with diffusive reflection conditions at the boundary. In an appropriate singular limit corresponding to small Knudsen number and long time…

Short wave equations were introduced in connection with the nonlinear reflection of weak shock waves. They also relate to the modulation of a gas-fluid mixture. Khokhlov-Zabolotskaya equation are used to describe the propagation of a…

We introduce a generalized similarity analysis which grants a qualitative description of the localised solutions of any nonlinear differential equation. This procedure provides relations between amplitude, width, and velocity of the…

We study the existence of stationary solutions for a nonlocal version of the Fisher-Kolmogorov-Petrovskii-Piscounov (FKPP) equation. The main motivation is a recent study by Berestycki et {al.} [Nonlinearity 22 (2009), {pp.}~2813--2844]…

We study the global existence and uniqueness of weak solutions to kinetic Kolmogorov-Vicsek models that can be considered a non-local non-linear Fokker-Planck type equation describing the dynamics of individuals with orientational…