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Nonlocal Symmetries, Consistent Riccati Expansion Solvability and Interaction Solutions of the Generalized Ito Equation
In this paper, we investigate the generalized Ito equation. By using the truncated Painlevé analysis method, we successfully derive its nonlocal...
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Bifurcation and Turing instability for a freshwater tussock sedge model with nonlocal interaction
The Hopf bifurcation, Turing instability and steady state bifurcation to a fresh-water tussock sedge model with nonlocal interaction under Neumman...
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Thermo-Hydro-Mechanical Interaction in a Poroelastic Half-Space with Nonlocal Memory Effects
The present analysis aims to develop a new mathematical model describing hydro-mechanical interaction based on the nonlocal theory proposed by...
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Solitary traveling waves in Fermi-Pasta-Ulam-type systems with nonlocal interaction on a 2D lattice
The article deals with the Fermi-Pasta-Ulam-type systems that describe an infinite system of particles with nonlocal interaction on a two-dimensional...
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Approximation by Nonlocal Problems
In this Chapter we study a nonlocal counterpart of the least gradient problem, i.e. the minimization of the functional...
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Nonlocal Integrable Equations in Soliton Theory
This article is to provide a brief overview of the study of nonlocal integrable equations in soliton theory. The concept of nonlocality is explained,...
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Local and Nonlocal Liquid Drop Models
We consider some extensions of Gamow’s liquid drop model for an atomic nucleus. We present a review of the classical model, and then we illustrate...
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Nonlocal Diffusion Models with Consistent Local and Fractional Limits
For some spatially nonlocal diffusion models with a finite range of nonlocal interactions measured by a positive parameter...
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Nonlocal capillarity for anisotropic kernels
We study a nonlocal capillarity problem with interaction kernels that are possibly anisotropic and not necessarily invariant under scaling. In...
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Nonlocal approximation of nonlinear diffusion equations
We show that degenerate nonlinear diffusion equations can be asymptotically obtained as a limit from a class of nonlocal partial differential...
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Nonlocal Wasserstein distance: metric and asymptotic properties
The seminal result of Benamou and Brenier provides a characterization of the Wasserstein distance as the path of the minimal action in the space of...
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Reduced Variance Random Batch Methods for Nonlocal PDEs
Random Batch Methods (RBM) for mean-field interacting particle systems enable the reduction of the quadratic computational cost associated with...
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Shape optimization for interface identification in nonlocal models
Shape optimization methods have been proven useful for identifying interfaces in models governed by partial differential equations. Here we consider...
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Unified two-phase nonlocal formulation for vibration of functionally graded beams resting on nonlocal viscoelastic Winkler-Pasternak foundation
A nonlocal study of the vibration responses of functionally graded (FG) beams supported by a viscoelastic Winkler-Pasternak foundation is presented....
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A new nonlocal calculus framework. Helmholtz decompositions, properties, and convergence for nonlocal operators in the limit of the vanishing horizon
We introduce a new nonlocal calculus framework which parallels (and includes as a limiting case) the differential setting. The integral operators...
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Cognitive Consumer-Resource Spatiotemporal Dynamics with Nonlocal Perception
Nonlocal perception is crucial to the mechanistic modeling of cognitive animal movement. We formulate a diffusive consumer-resource model with...
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Gamma-convergence of a nonlocal perimeter arising in adversarial machine learning
In this paper we prove Gamma-convergence of a nonlocal perimeter of Minkowski type to a local anisotropic perimeter. The nonlocal model describes the...
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Nonlinear semigroups for nonlocal conservation laws
We investigate a class of nonlocal conservation laws in several space dimensions, where the continuum average of weighted nonlocal interactions are...
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Nonlocal Green Theorems and Helmholtz Decompositions for Truncated Fractional Gradients
In this work we further develop a nonlocal calculus theory (initially introduced in Bellido et al. (Adv Nonlinear Anal 12:20220316, 2023)) associated...
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Optimal Control of Nonlocal Continuity Equations: Numerical Solution
The paper addresses an optimal ensemble control problem for nonlocal continuity equations on the space of probability measures. We admit the general...
