Boundary fluxes for nonlocal diffusion

By Carmen Cortázar, Manuel Elgueta, Julio D. Rossi, Noemi Wolanski. 2007

126 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/20585adc89c8dba8eddef11f4fa29e7e2c3cef30

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In Applied Mathematics

In Computational Theory and Mathematics

In Control and Systems Engineering

Citations in the corpus

How to Approximate the Heat Equation with Neumann Boundary Conditions by Nonlocal Diffusion Problems (2006, background): “As in [ 7 ] and [8], existence and uniqueness will be a consequence of Banach’s fixed point theorem.”
A logistic equation with refuge and nonlocal diffusion (2009, background): “the “Neumann” boundary condition for the same problem is treated in [1], [13] and [14].”
A nonlocal p-Laplacian evolution equation with Neumann boundary conditions (2008, methodology): “and variations of it, have been recently widely used to model diusion processes, see [7], [8], [10], [17], [18], [19], [ 21 ], [25], [26], [29], [31] and [34].”
The Neumann problem for nonlocal nonlinear diffusion equations (2008, methodology): “In [10] and [12] the asymptotic behaviour for the linear model is studied and in [13] it is proved that solutions to the linear problem converge to the solution of the classical heat equation with Neumann boundary conditions when the convolution kernel J is rescaled in a suitable way.”
Nonlocal Kirchhoff diffusion problems: local existence and blow-up of solutions (2018, background): “For recent references on nonlocal diffusion problems, see [3, 9, 12, 34].”
On the principal eigenvalue of some nonlocal diffusion problems (2009, background): “This is indeed the case at least for some nonlinearities, even for the parabolic version, see [15], [16], [17], [20].”
Nonlocal problems with Neumann boundary conditions (2014, background): “5) Other Neumann problems for the fractional Laplacian (or other nonlocal operators) were introduced in [4, 8], [1, 3], [9, 10, 11], and [15].”
A nonlocal convection–diffusion equation (2007, background): “Moreover, in [8] and [9] nonlocal Neumann boundary conditions where taken into account.”
Blow-up for a non-local diffusion problem with Neumann boundary conditions and a reaction term (2009, methodology): “Non-local evolution equations of the form ut (x, t) = ∫ RN J (x−y)u(y, t) dy−u(x, t), and their variations, have been widely used to model diffusion processes, see [1–4,6–8,10–14,18].”
Asymptotic behavior for nonlocal diffusion equations (2006, background): “As stated in [16], if u(x,t) is thought of as the density of a single population at the point x at time t , and J(x − y) is thought of as the probability distribution of jumping from location y to location x , then (J ∗ u)(x,t) = (cid:2) R N J(y − x)u(y,t) d y is the rate at which individuals are…”