On a Problem of Cross-Diffusion with Nonlocal Boundary Conditions

On a Class of Nonlinear Reaction-diffusion Systems with Nonlocal Boundary Conditions

In the recent years, a new attention has been given to reaction-diffusion systems which involve an integral over the spatial domain of a function of the desired solution on the boundary conditions; see [2, 5, 7, 6, 9, 10, 17, 18, 19, 20, 22] and the references cited therein. Most of the studied problems in the current literature are devoted to problems which combine a classical boundary conditi...

On a nonlocal problem with integral boundary conditions for a multidimensional elliptic equation

A third-order nonlocal problem with nonlocal conditions

Nonlocal Problems with Neumann Boundary Conditions

We introduce a new Neumann problem for the fractional Laplacian arising from a simple probabilistic consideration, and we discuss the basic properties of this model. We can consider both elliptic and parabolic equations in any domain. In addition, we formulate problems with nonhomogeneous Neumann conditions, and also with mixed Dirichlet and Neumann conditions, all of them having a clear probab...

Numerical solution of time-dependent diffusion equations with nonlocal boundary conditions via a fast matrix approach

One-dimensional parabolic equation; Nonlocal boundary conditions; Taylor approximation; Operational matrices; Krylov subspace iterative methods; Restarted GMRES Abstract This article contributes a matrix approach by using Taylor approximation to obtain the numerical solution of one-dimensional time-dependent parabolic partial differential equations (PDEs) subject to nonlocal boundary integral c...