Related papers: Well-posedness of aggregation-diffusion systems wi…
We prove the existence of solutions to a non-linear, non-local, degenerate equation which was previously derived as the formal hydrodynamic limit of an active Brownian particle system, where the particles are endowed with a position and an…
We investigate stationary solutions of a non-local aggregation equation with degenerate power-law diffusion and bounded attractive potential in arbitrary dimensions. Compact stationary solutions are characterized and compactness…
We prove local existence and uniqueness results for the (space-homogeneous) 4-wave kinetic equation in wave turbulence theory. We consider collision operators defined by radial, but general dispersion relations satisfying suitable bounds,…
Given sufficiently regular data \textit{without} decay assumptions at infinity, we prove local well-posedness for non-linear dispersive equations of the form \[ \partial_t u + \mathsf A(\nabla) u + \mathcal Q(|u|^2) \cdot \nabla u= \mathcal…
We consider a class of Cahn-Hilliard equation with kinetic rate dependent dynamic boundary conditions that describe possible short-range interactions between the binary mixture and the solid boundary. In the presence of surface diffusion on…
We study the well-posedness of the initial value problem on periodic intervals for linear and quasilinear evolution equations for which the leading-order terms have three spatial derivatives. In such equations, there is a competition…
In this paper, we investigate the well-posedness of weak solutions to the time-fractional Fokker-Planck equation. Its dynamics is governed by anomalous diffusion, and we consider the most general case of space-time dependent forces.…
Weakly nonlinear amplitude equations are derived for the onset of spatially extended patterns on a general class of n-component bulk-surface reaction-diffusion systems in a ball, under the assumption of linear kinetics in the bulk and…
We consider an aggregation-diffusion equation modelling particle interaction with non-linear diffusion and non-local attractive interaction using a homogeneous kernel (singular and non-singular) leading to variants of the Keller-Segel model…
Local and global well-posedness of the coagulation-fragmentation equation with size diffusion are investigated. Owing to the semilinear structure of the equation, a semigroup approach is used, building upon generation results previously…
A global existence theorem on weak solutions is shown for the continuous coagulation equation with collisional breakage under certain classes of unbounded collision kernels and distribution functions. This model describes the dynamics of…
The primary objective of this paper is to investigate the well-posedness theories associated with the discrete nonlinear Schr\"odinger equation and Klein-Gordon equation. These theories encompass both local and global well-posedness, as…
An existence result on weak solutions to the continuous coagulation equation with collision-induced multiple fragmentation is established for certain classes of unbounded coagulation, collision and breakup kernels. In this model, a pair of…
We study a class of degenerate convection diffusion equations with a fractional nonlinear diffusion term. These equations are natural generalizations of anomalous diffusion equations, fractional conservations laws, local convection…
In this paper we investigate qualitative and asymptotic behavior of solutions for a class of diffusion-aggregation equations. Most results except the ones in section 3 and 6 concern radial solutions. The challenge in the analysis consists…
An attempt is made to find a comprehensive mathematical framework in which to investigate the problems of well-posedness and asymptotic analysis for fully nonlinear evolutionary game theoretic models. The model should be rich enough to…
In this article, we investigate the existence and uniqueness of weak solutions to the continuous coagulation equation with collisional breakage for a class of unbounded collision kernels and distribution function. The collision kernels and…
We give a comprehensive study of the analytic properties and long-time behavior of solutions of a reaction-diffusion system in a bounded domain in the case where the nonlinearity satisfies the standard monotonicity assumption. We pay the…
Global well-posedness and exponential decay to equilibrium are proved for the homogeneous Landau equation from kinetic theory. The initial distribution is only assumed to be bounded and decaying sufficiently fast at infinity. In particular,…
We consider the aggregation equation $\rho_{t}-\nabla\cdot(\rho\nabla K\ast\rho) =0$ in $\mathbb{R}^{n}$, where the interaction potential $K$ incorporates short-range Newtonian repulsion and long-range power-law attraction. We study the…