相关论文: Concentration limit for non-local dissipative conv…

We show that locally bounded, local weak solutions to certain nonlocal, nonlinear diffusion equations modeled on the fractional porous media and fast diffusion equations given by \begin{align*} \partial_t u + (-\Delta)^s(|u|^{m-1}u) = 0…

We present a convergence result from nonlocal to local behavior for a system of nonlocal balance laws. The velocity field of the underlying conservation laws is diagonal. In contrast, the coupling to the remaining balance laws involves a…

This paper provides a unified mathematical analysis of a family of non-local diffuse interface models for tumor growth describing evolutions driven by long-range interactions. These integro-partial differential equations model cell-to-cell…

Over the past decades, nonlocal models have been widely used to describe aggregation phenomena in biology, physics, engineering, and the social sciences. These are often derived as mean-field limits of attraction-repulsion agent-based…

In this paper, we proceed to study the nonlocal diffusion problem proposed by Li and Wang [8], where the left boundary is fixed, while the right boundary is a nonlocal free boundary. We first give some accurate estimates on the longtime…

We study the existence and uniqueness of mild and strong solutions of nonlocal nonlinear diffusion problems of $p$-Laplacian type with nonlinear boundary conditions posed in metric random walk spaces. These spaces include, among others,…

In this paper we consider a one-dimensional nonlocal interaction equation with quadratic porous-medium type diffusion in which the interaction kernels are attractive, nonnegative, and integrable on the real line. Earlier results in the…

We study the large-time behaviour of the solutions $u$ of the evolution equation involving nonlinear diffusion and gradient absorption $\partial_t u - \Delta_p u + |\nabla u|^q=0$. We consider the problem posed for $x\in {\mathbb R}^N $ and…

In this paper we study a broad class of non-local advection-diffusion models describing the behaviour of an arbitrary number of interacting species, each moving in response to the non-local presence of others. Our model allows for different…

This paper investigates degenerate nonlocal free boundary problems arising in the context of superconductivity, extending the nonlocal counterpart to the work of Caffarelli, Salazar, and Shahgholian \cite{CS02, CSS04} in the local setting.…

The Cahn--Hilliard equation is one of the most common models to describe phase segregation processes in binary mixtures. In recent times, various dynamic boundary conditions have been introduced to model interactions of the materials with…

We consider a nonlocal aggregation diffusion equation incorporating repulsion modelled by nonlinear diffusion and attraction modelled by nonlocal interaction. When the attractive interaction kernel is radially symmetric and strictly…

Well-posedness in $L_\infty$ of the nonlocal Gray-Scott model is studied for integrable kernels, along with the stability of the semi-trivial spatially homogeneous steady state. In addition, it is shown that the solutions to the nonlocal…

In this note, we propose a discrete model to study one-dimensional transport equations with non-local drift and supercritical dissipation. The inspiration for our model is the equation $$ \theta_t + (H\theta) \theta_x +(-\Delta)^\alpha…

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…

The existence of global weak solutions to a parabolic energy-transport system in a bounded domain with no-flux boundary conditions is proved. The model can be derived in the diffusion limit from a kinetic equation with a linear collision…

We consider the problem of the homogenization of non-local quadratic energies defined on $\delta$-periodic disconnected sets defined by a double integral, depending on a kernel concentrated at scale $\varepsilon$. For kernels with unbounded…

We propose algorithms for solving convective-diffusion partial differential equations (PDEs), which model surfactant concentration and heat transport on evolving surfaces, based on intrinsic kernel-based meshless collocation methods. The…

We develop general heterogeneous nonlocal diffusion models and investigate their connection to local diffusion models by taking a singular limit of focusing kernels. We reveal the link between the two groups of diffusion equations which…

When canonical Hamiltonians of local quantum field theories are transformed using a renormalization group procedure for effective particles, the resulting interaction terms are non-local. The range of their non-locality depends on the…