We propose a new edge preserving image deconvolution model by combining total variation and nonlocal means regularization. Natural images exhibit an high degree of redundancy. Using this redundancy, the nonlocal means regularization strategy is a good technique for detail preserving image restoration. In order to further improve the visual quality of the nonlocal means based algorithm, total va...

We study a weakly local, but nonlocal model in spacetime dimension d ≥ 2 and prove that it is maximally nonlocal in a certain specific quantitative sense. Nevertheless, depending on the number of dimensions d, it has string–localized or brane–localized operators which commute at spatial distances. In two spacetime dimensions, the model even comprises a covariant and local subnet of operators lo...

In this study, the mechanical buckling response of refined hyperbolic shear deformable (FG) functionally graded nanobeams embedded in an elastic foundation is investigated based on the refined hyperbolic shear deformation theory. Material properties of the FG nanobeam change continuously in the thickness direction based on the power-law model. To capture small size effects, Eringen’s nonlocal e...

Size-dependent longitudinal and torsional vibrations of nano-beams are examined by two-phase mixture integral elasticity. A new and efficient elastodynamic model is conceived by convexly combining the local phase with strain- and stress-driven purely nonlocal phases. The proposed stress-driven nonlocal integral mixture leads to well-posed structural problems for any value of the scale parameter...

This paper investigates a nonlocal version of a model for phase separation on an atomic lattice that was introduced by P. Podio-Guidugli in Ric. Mat. 55 (2006) 105-118. The model consists of an initial-boundary value problem for a nonlinearly coupled system of two partial differential equations governing the evolution of an order parameter ρ and the chemical potential μ. Singular contributions ...

The paper deals with the problem of nonlocal generalization of constitutive models such as microplane model M4 for concrete, in which the yield limits, called stress–strain boundaries, are softening functions of the total strain. Such constitutive models call for a different nonlocal generalization than those for continuum damage mechanics, in which the total strain is reversible, or for plasti...

We prove Dirichlet’s principle for a nonlocal p-Laplacian system which arises in the nonlocal setting of peridynamics when p = 2. This nonlinear model includes boundary conditions imposed on a nonzero volume collar surrounding the domain. Our analysis uses nonlocal versions of integration by parts techniques that resemble the classical Green and Gauss identities. The nonlocal energy functional ...

We investigate the singularity formation of a nonlinear nonlocal system. This nonlocal system is a simplified one-dimensional system of the 3D model that was recently proposed by Hou and Lei (Comm Pure Appl Math 62(4):501–564, 2009) for axisymmetric 3D incompressible Navier–Stokes equations with swirl. The main difference between the 3D model of Hou and Lei and the reformulated 3D Navier– Stoke...

In this paper, a scalar peridynamic model is analyzed. The study extends earlier works in the literature on nonlocal diffusion and nonlocal peridynamic models to include a sign changing kernel. We prove the well-posedness of both variational problems with volume constraints and time-dependent equations with or without damping. The analysis is based on some nonlocal Poincaré type inequalities an...

In this work we model and numerically analyse, the dynamics of a single species food-limited model with delay, we focus in the asymptotic behavior. We use the sub and supersolutions method to provide some numerical simulations of the asymptotic behavior for several cases, autonomous, periodic, almost periodic concluding with a model that incoporates nonlocal delays as well as a continuous delay...