Results 11 to 20 of about 3,306 (214)
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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Numerical Methods for a Diffusive Class of Nonlocal Operators [PDF]
Journal of Scientific Computing, 2021 In this paper we develop a numerical scheme based on quadratures to approximate solutions of integro-differential equations involving convolution kernels, $ν$, of diffusive type. In particular, we assume $ν$ is symmetric and exponentially decaying at infinity. We consider problems posed in bounded domains and in $\R$.
Gabriela Jaramillo +2 more
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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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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 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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Nonlocal Neural Networks, Nonlocal Diffusion and Nonlocal Modeling
CoRR, 2018 Nonlocal neural networks have been proposed and shown to be effective in several computer vision tasks, where the nonlocal operations can directly capture long-range dependencies in the feature space. In this paper, we study the nature of diffusion and damping effect of nonlocal networks by doing spectrum analysis on the weight matrices of the well ...
Yunzhe Tao +3 more
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Nonlocal diffusion equations in Carnot groups
Rendiconti del Circolo Matematico di Palermo Series 2, 2022 20 ...
Isolda E. Cardoso, Raúl E. Vidal
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Travelling Wavefronts in Nonlocal Diffusion Equations with Nonlocal Delay Effects [PDF]
Bulletin of the Malaysian Mathematical Sciences Society, 2017 This paper deals with the existence, monotonicity, uniqueness and asymptotic behaviour of travelling wavefronts for a class of temporally delayed, spatially nonlocal diffusion equations.
Shangjiang Guo, Johannes Zimmer
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Dynamics of a nonlocal SIR epidemic model with free boundaries
Franklin Open, 2023 This paper is devoted to a nonlocal SIR type epidemic model, with free boundary denoting the expanding front. We aim to examine the full information about the dynamical behaviors of the involved disease that caused by the nonlocal diffusion and growing ...
Jia-Feng Cao +3 more
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Isoperimetric inequalities in nonlocal diffusion problems with integrable kernel [PDF]
Opuscula MathematicaWe deduce isoperimetric estimates for solutions of linear stationary and evolution problems. Our main result establishes the comparison in norm between the solution of a problem and its symmetric version when nonlocal diffusion defined through integrable
Gonzalo Galiano
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