Related papers: Regularity and mass conservation for discrete coag…
The global existence of bounded solutions to reaction-diffusion systems with fractional diffusion in the whole space $\mathbb R^N$ is investigated. The systems are assumed to preserve the non-negativity of initial data and to dissipate…
A mathematical model for the discrete nonlinear fragmentation (collision-induced breakage) equation with diffusion is studied. The existence of global weak solutions is established in arbitrary spatial dimensions without assuming a strictly…
We propose boundary conditions for the diffusion equation that maintain the initial mean and the total mass of a discrete data sample in the density estimation process. A complete study of this framework with numerical experiments using the…
In this paper, we investigate the use of so called "duality lemmas" to study the system of discrete coagulation-fragmentation equations with diffusion. When the fragmentation is strong enough with respect to the coagulation, we show that we…
The asymptotic behavior of the solution of an infinite set of Smoluchowski's discrete coagulation-fragmentation-diffusion equations with non-homogeneous Neumann boundary conditions, defined in a periodically perforated domain, is analyzed.…
In this paper we study the discrete coagulation--fragmentation models with growth, decay and sedimentation. We demonstrate the existence and uniqueness of classical global solutions provided the linear processes are sufficiently strong.…
In this paper, we study the asymptotic estimate of solution for a mixed-order time-fractional diffusion equation in a bounded domain subject to the homogeneous Dirichlet boundary condition. Firstly, the unique existence and regularity…
We examine the validity of the principle of mass conservation for solutions of some typical equations in the theory of nonlinear diffusion, including equations in standard differential form and also their fractional counterparts. In Part 1,…
This paper is devoted to the analysis of a numerical scheme for the coagulation and fragmentation equation with diffusion in space. A finite volume scheme is developed, based on a conservative formulation of the space nonhomogeneous…
Although the spatially continuous version of the reaction-diffusion equation has been well studied, in some instances a spatially-discretized representation provides a more realistic approximation of biological processes. Indeed,…
We consider a class of reaction-diffusion equations with a stochastic perturbation on the boundary. We show that in the limit of fast diffusion, one can rigorously approximate solutions of the system of PDEs with stochastic Neumann boundary…
We consider a nonlinear drift-diffusion system for multiple charged species in a porous medium in 2D and 3D with periodic microstructure. The system consists of a transport equation for the concentration of the species and Poisson's…
We consider the inverse problem of determining different type of information about a diffusion process, described by ordinary or fractional diffusion equations stated on a bounded domain, like the density of the medium or the velocity field…
We prove optimal boundary regularity for bounded positive weak solutions of fast diffusion equations in smooth bounded domains. This solves a problem raised by Berryman and Holland in 1980 for these equations in the subcritical and critical…
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…
In this paper we study the continuous coagulation and multiple fragmentation equation for the mean-field description of a system of particles taking into account the combined effect of the coagulation and the fragmentation processes in…
We study the global existence and uniform-in-time bounds of classical solutions in all dimensions to reaction-diffusion systems dissipating mass. By utilizing the duality method and the regularization of the heat operator, we show that if…
We investigate the fractional diffusion approximation of a kinetic equation set in a bounded interval with diffusive reflection conditions at the boundary. In an appropriate singular limit corresponding to small Knudsen number and long time…
A solution is developed for a convection-diffusion equation describing chemical transport with sorption, decay, and production. The problem is formulated in a finite domain where the appropriate conservation law yields Robin conditions at…
This article deals with an initial-boundary value problem for the coupled chemotaxis-haptotaxis system with nonlinear diffusion \begin{align*} u_t=&\nabla\cdot(D(u)\nabla u)-\chi\nabla\cdot(u\nabla v)-\xi\nabla\cdot(u\nabla w)+\mu…