The main goal of this paper is to prove existence and non-existence results for deterministic Kardar–Parisi–Zhang type equations involving non-local “gradient terms”. More precisely, let \(\Omega \subset \mathbb {R}^N\), \(N \ge 2\), be a bounded domain with boundary \(\partial \Omega \) class \(C^2\). For \(s \in (0,1)\), we consider problems the form $$\begin{aligned} \left\{ \begin{aligned} ...

The finite element simulation of forming processes or vehicle crash scenarios involves multiaxial loading conditions in general. Thereby, damage and failure ductile steel sheets is triggered by void growth under hydrostatic tensile elongation within a narrow band shear dominated loading. These different mechanisms are considered stress state dependent continuum model. initiation represented cri...

Abstract The size-dependent band structure of an Si phononic crystal (PnC) slab with air hole is studied by utilizing the non-classic wave equations nonlocal strain gradient theory (NSGT). three-dimensional (3D) for anisotropic material are derived according to differential form NSGT. Based on general partial equation modules in COMSOL, a method proposed solve equations. bands in-plane modes an...

Buckling analysis of a functionally graded (FG) nanobeam resting on two-parameter elastic foundation is presented based on third-order shear deformation beam theory (TOSDBT). The in-plane displacement of TOSDBT has parabolic variation through the beam thickness. Also, TOSDBT accounts for shear deformation effect and verifies stress-free boundary conditions on upper and lower faces of FG nanobea...

We consider a congested aggregation model that describes the evolution of a density through the competing effects of nonlocal Newtonian attraction and a hard height constraint. This provides a counterpoint to existing literature on repulsive-attractive nonlocal interaction models, where the repulsive effects instead arise from an interaction kernel or the addition of diffusion. We formulate our...

deflection analysis of a simply supported microbeam subjected to a concentrated load at the middle is investigated on the basis of a shear deformable beam theory and non-classical theory. effects of shear deformation and small size are taken into consideration by hyperbolic shear deformable beam theory and modified strain gradient theory, respectively. the governing differential equations and c...