Results 1 to 10 of about 37,564 (233)
Path Laplacians versus fractional Laplacians as nonlocal operators on networks
New Journal of Physics, 2021 Here we study and compare nonlocal diffusion processes on networks based on two different kinds of Laplacian operators. We prove that a nonlocal diffusion process on a network based on the path Laplacian operator always converges faster than the standard
Ernesto Estrada
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Formulation, analysis and computation of an optimization-based local-to-nonlocal coupling method
Results in Applied Mathematics, 2021 We present an optimization-based coupling method for local and nonlocal continuum models. Our approach couches the coupling of the models into a control problem where the states are the solutions of the nonlocal and local equations, the objective is to ...
Marta D’Elia, Pavel Bochev
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A Review of Local-to-Nonlocal Coupling Methods in Nonlocal Diffusion and Nonlocal Mechanics [PDF]
Journal of Peridynamics and Nonlocal Modeling, 2021 Local-to-Nonlocal (LtN) coupling refers to a class of methods aimed at combining nonlocal and local modeling descriptions of a given system into a unified coupled representation. This allows to consolidate the accuracy of nonlocal models with the computational expediency of their local counterparts, while often simultaneously removing additional ...
Marta D’Elia +4 more
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Nonlocal diffusion equations in Carnot groups
Rendiconti del Circolo Matematico di Palermo Series 2, 2022 Let $G$ be a Carnot group. We study nonlocal diffusion equations in a domain $ $ of $G$ of the form $$ u_t^ (x,t)=\int_{G}\frac{1}{ ^2}K_ (x,y)(u^ (y,t)-u^ (x,t))\,dy, \qquad x\in $$ with $u^ =g(x,t)$ for $x\notin $. For appropriate rescaled kernel $K_ $ we prove that solutions $u^ $, when $ \rightarrow0$, uniformly approximate the ...
Isolda E. Cardoso, Raúl E. Vidal
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Nonlocal Diffusion and Applications [PDF]
, 2016 Working in the fractional Laplace framework, this book provides models and theorems related to nonlocal diffusion phenomena. In addition to a simple probabilistic interpretation, some applications to water waves, crystal dislocations, nonlocal phase transitions, nonlocal minimal surfaces and Schrödinger equations are given.
Bucur, Claudia and Valdinoci, Enrico
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Effective nonlocal kernels on reaction–diffusion networks
Journal of Theoretical Biology, 2021 A new method to derive an essential integral kernel from any given reaction-diffusion network is proposed. Any network describing metabolites or signals with arbitrary many factors can be reduced to a single or a simpler system of integro-differential equations called "effective equation" including the reduced integral kernel (called "effective kernel"
Shin-Ichiro Ei +4 more
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Propagation and reaction–diffusion models with free boundaries
Bulletin of Mathematical Sciences, 2022 In this short survey, we describe some recent developments on the modeling of propagation by reaction-differential equations with free boundaries, which involve local as well as nonlocal diffusion.
Yihong Du
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A local/nonlocal diffusion model [PDF]
Applicable Analysis, 2021 In this paper, we study some qualitative properties for an evolution problem that combines local and nonlocal diffusion operators acting in two different subdomains and, coupled in such a way that, the resulting evolution problem is the gradient flow of an energy functional.
Santos, Bruna C. dos +2 more
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A Strong Maximum Principle for Nonlinear Nonlocal Diffusion Equations
Axioms, 2023 We consider a class of nonlinear integro-differential equations that model degenerate nonlocal diffusion. We investigate whether the strong maximum principle is valid for this nonlocal equation. For degenerate parabolic PDEs, the strong maximum principle
Tucker Hartland, Ravi Shankar
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A logistic equation with nonlocal interactions [PDF]
, 2016 We consider here a logistic equation, modeling processes of nonlocal character both in the diffusion and proliferation terms. More precisely, for populations that propagate according to a L\'evy process and can reach resources in a neighborhood of ...
Caffarelli, Luis +2 more
core +4 more sources