Local and Nonlocal Energy-Based Coupling Models

@article{Acosta2021LocalAN,
  title={Local and Nonlocal Energy-Based Coupling Models},
  author={Gabriel Acosta and Francisco M. Bersetche and Julio D. Rossi},
  journal={SIAM Journal on Mathematical Analysis},
  year={2021}
}
In this paper we study two different ways of coupling a local operator with a nonlocal one in such a way that the resulting equation is related to an energy functional. In the first strategy the coupling is given via source terms in the equation and in the second one a flux condition in the local part appears. For both models we prove existence and uniqueness of a solution that is obtained via direct minimization of the related energy functional. In the second part of this paper we extend these… 
1 Citations

Figures from this paper

Coupling local and nonlocal equations with Neumann boundary conditions

We introduce two different ways of coupling local and nonlocal equations with Neumann boundary conditions in such a way that the resulting model is naturally associated with an energy functional. For

References

SHOWING 1-10 OF 43 REFERENCES

A local/nonlocal diffusion model

ABSTRACT In this paper, we study some qualitative properties for solutions to an evolution problem that combines local and nonlocal diffusion operators acting in two different subdomains. The

Coupling local and nonlocal evolution equations

We prove existence, uniqueness and several qualitative properties for evolution equations that combine local and nonlocal diffusion operators acting in different subdomains and coupled in such a way

Regularity for a Local–Nonlocal Transmission Problem

We formulate and study an elliptic transmission-like problem combining local and nonlocal elements. Let $${\mathbb{R}^n}$$Rn be separated into two components by a smooth hypersurface Γ. On one side

On a non-local equation arising in population dynamics

  • J. CovilleL. Dupaigne
  • Mathematics
    Proceedings of the Royal Society of Edinburgh: Section A Mathematics
  • 2007
We study a one-dimensional non-local variant of Fisher's equation describing the spatial spread of a mutant in a given population, and its generalization to the so-called monostable nonlinearity. The

The bond-based peridynamic system with Dirichlet-type volume constraint

  • Tadele MengeshaQ. Du
  • Mathematics
    Proceedings of the Royal Society of Edinburgh: Section A Mathematics
  • 2014
In this paper, the bond-based peridynamic system is analysed as a non-local boundary-value problem with volume constraint. The study extends earlier works in the literature on non-local diffusion and

A Quasi-nonlocal Coupling Method for Nonlocal and Local Diffusion Models

The idea of “geometric reconstruction” is extended to couple a nonlocal diffusion model directly with the classical local diffusion in one dimensional space and this new coupling framewor...

From local to nonlocal in a diffusion model

In this paper we investigate the behaviour of a di usion equation where di usion depends to nonlocal terms. In a radial setting, by regarding bifurcation theory, we prove the existence of local

Coupling of nonlocal and local continuum models by the Arlequin approach

The objective of this work is to develop and apply the Arlequin framework to couple nonlocal and local continuum mechanical models. A mechanically‐based model of nonlocal elasticity, which involves

How to Approximate the Heat Equation with Neumann Boundary Conditions by Nonlocal Diffusion Problems

We present a model for nonlocal diffusion with Neumann boundary conditions in a bounded smooth domain prescribing the flux through the boundary. We study the limit of this family of nonlocal