Related papers: Non-local parallel transport in BOUT++
This article deals with a class of chemotaxis systems describing mechanisms from mathematical biology. In the specific, for a rather general class of attraction-repulsion models, with nonlinear productions, diffusion, sensitivities and…
Writing the boundary integral equation for an exterior problem of elasticity is subordinate so far to hypotheses on the asymptotical behaviour at infinity of solutions. The sufficient conditions met in the literature are too restrictive and…
Local-nonlocal coupling approaches provide a means to combine the computational efficiency of local models and the accuracy of nonlocal models. This paper studies the continuous and discrete formulations of three existing approaches for the…
Extending the famous Model B for the time evolution of a liquid mixture, we derive an approximate expression for the mobility matrix that couples the different mixture components. This approach is based on a single component fluid with…
Comparing with the classical local gradient flow and phase field models, the nonlocal models such as nonlocal Cahn-Hilliard equations equipped with nonlocal diffusion operator can describe more practical phenomena for modeling phase…
We study the existence of nonnegative solutions for a system of impulsive differential equations subject to nonlinear, nonlocal boundary conditions. The system presents a coupling in the differential equation and in the boundary conditions.…
We consider dynamic boundary conditions involving non-local operators. Our analysis includes a detailed description of such operators together with their relations with random times and random (additive) functionals. We provide some new…
We study a class of nonlocal, energy-driven dynamical models that govern the motion of closed, embedded curves from both an energetic and dynamical perspective. Our energetic results provide a variety of ways to understand physically…
Transport-dominated partial differential equation models have been used extensively over the past two decades to describe various collective migration phenomena in cell biology and ecology. To understand the behaviour of these models (and…
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…
A nonlocal field theory of peridynamic type is applied to model the brittle fracture problem. The elastic fields obtained from the nonlocal model are shown to converge in the limit of vanishing non-locality to solutions of classic plane…
This paper deals with the modeling and numerical simulations of multilane vehicular traffic according to the discrete kinetic theory approach. The nonlinear additive interactions and external actions such as tollgates as well traffic signs…
By topological arguments, we prove new results on the existence, non-existence, localization and multiplicity of nontrivial solutions of a class of perturbed nonlinear integral equations. These type of integral equations arise, for example,…
In this paper we continue to study a non-local free boundary problem arising in financial bubbles. We focus on the parabolic counterpart of the bubble problem and suggest an iterative algorithm which consists of a sequence of parabolic…
We investigate the existence of solutions of constrained nonlinear differential inclusions with nonlocal boundary conditions. Our viability theorems are based on the assumption that the right-hand side of differential inclusion is defined…
We prove the well posedness of a class of non linear and non local mixed hyperbolic-parabolic systems in bounded domains, with Dirichlet boundary conditions. In view of control problems, stability estimates on the dependence of solutions on…
We discuss the relation between entanglement and nonlocality in the hidden nonlocality scenario. Hidden nonlocality signifies nonlocality that can be activated by applying local filters to a particular state that admits a local…
The shallow water equations often assume a constant velocity profile along the vertical axis. However, this assumption does not hold in many practical applications. To better approximate the vertical velocity distribution, models such as…
The paper deals with second order parabolic equations on bounded domains with Dirichlet conditions in arbitrary Euclidean spaces. Their interest comes from being models for describing reaction-diffusion processes in several frameworks. A…
The position-based dynamics (PBD) algorithm is a popular and versatile technique for real-time simulation of deformable bodies, but is only applicable to forces that can be expressed as linearly compliant constraints. In this work, we…