The study of the stress-strain state a thermoelastic hollow cylinder with homogeneous coating is carried out taking into account scale effects. Aifantis' one-parameter gradient model used to for Equilibrium equations and boundary conditions composite are obtained on basis Lagrange variational principle. In comparison classical formulation problem, additional conjugation set moment stresses disp...

The packing of hard-core particles in contact with their neighbors is a statically determinate problem. probability functional method allows deriving the full system equations for stress tensor components analytically. For an isotropic and homogeneous two-dimensional packing, we derive classical Euler–Cauchy Navier equations; latter expressing terms Airy function.

The existence of proper weak solutions of the Dirichlet-Cauchy problem constituted by the Navier-Stokes-Fourier system which characterizes the incompressible homogeneous Newtonian fluids under thermal effects is studied. We call proper weak solutions such weak solutions that verify some local energy inequalities in analogy with the suitable weak solutions for the Navier-Stokes equations. Finall...

and Applied Analysis 3 Mu et al. 19 studied the secondary critical exponent for the following p-Laplacian equation with slow decay initial values: ut div ( |∇u|p−2∇u ) u, x, t ∈ R × 0, T , u x, 0 u0 x , x ∈ R, 1.6 where p > 2, q > 1, and showed that, for q > q∗ c p − 1 p/N , there exists a secondary critical exponent ac p/ q 1 − p such that the solution u x, t of 1.6 blows up in finite time for...

where λ > 0 is a parameter, κ ∈ R is a constant, p = (N + 2)/(N − 2) is the critical Sobolev exponent, and f(x) is a non-homogeneous perturbation satisfying f ∈ H−1(Ω) and f ≥ 0, f ≡ 0 in Ω. Let κ1 be the first eigenvalue of −Δ with zero Dirichlet condition on Ω. Since (1.1)λ has no positive solution if κ ≤ −κ1 (see Remark 1 below), we will consider the case κ > −κ1. Let us recall the results f...