A nonlocal constitutive formulation for a porous ductile material is investigated, in which delocalizadon relates to the damage mechanism. An elastic-viscoplastic material model is used, with delocalization incorporated in terms of an integral condition on the rate of increase of the void volume fraction. Two model problems are analysed to study the effect of including this material length, one...

We establish conditions that guarantee Fredholm solvability in the Banach space Lp of nonlocal boundary value problems for elliptic abstract differential equations of the second order in an interval. Moreover, in the space L2 we prove in addition the coercive solvability, and the completeness of root functions (eigenfunctions and associated functions). The obtained results are then applied to t...

A new Lax representation for the Bogoyavlensky lattice is found, its r–matrix interpretation is elaborated. The r–matrix structure turns out to be related to a highly nonlocal quadratic Poisson structure on a direct sum of asso-ciative algebras. The theory of such nonlocal structures is developed, the Poisson property of the monodromy map is worked out in the most general situation. Some proble...

In this paper, a novel weighted nonlocal total variation (WNTV) method is proposed. Compared to the classical nonlocal total variation methods, our method modifies the energy functional to introduce a weight to balance between the labeled sets and unlabeled sets. With extensive numerical examples in semi-supervised clustering, image inpaiting and image colorization, we demonstrate that WNTV pro...

* Correspondence: zhgs917@163. com Nonlinear Scientific Research Center, Faculty of Science, Jiangsu University, Zhenjiang 212013, China Full list of author information is available at the end of the article Abstract This article deals with the blow-up problems of the positive solutions to a nonlinear parabolic equation with nonlocal source and nonlocal boundary condition. The blow-up and globa...

In this paper, nonlocal in time problem for abstract evolution equation of second order is studied and theorem on existence and uniqueness of its solution is proved. Some applications of this theorem for hyperbolic partial differential equations and systems are considered and it is proved, that well-posedness of the mentioned problems depends on algebraic properties of ratios between the dimens...

We develop and analyze an optimization–based method for the coupling of nonlocal and local diffusion problems with mixed volume constraints and boundary conditions. The approach formulates the coupling as a control problem where the states are the solutions of the nonlocal and local equations, the objective is to minimize their mismatch on the overlap of the nonlocal and local domains, and the ...

For the third order differential equation, y′′′ = f(x, y, y′, y′′), we consider uniqueness implies existence results for solutions satisfying the nonlocal 4-point boundary conditions, y(x1) = y1, y(x2) = y2, y(x3)− y(x4) = y3. Uniqueness of solutions of such boundary value problems is intimately related to solutions of the third order equation satisfying certain nonlocal 3-point boundary condit...

We investigate initial value problems for first-order difkreutial inclusions with nonlocal conditions. We provide conditions on the right-hand side that are suiBcieut for obtainlug a priori hounds on solutions. We then rely on a theorem of Bohneublust and Karlin to prove existeuce of at least one solution. @ 2002 Elseviir Science Ltd. All rights reserved. KeyWords-Differential inclusion, Nonloc...

Multiscale computational techniques in space and time are developed to study the impact response of thin, elastic, laminated composites. The displacement field is approximated using asymptotic expansion in space and time. Using the homogenization procedure in space and time, nonlocal membrane and bending equations of motion are derived. The nonlocal equations are stabilized to filter out the hi...