On a decay rate for a Landau-Ginzburg system with viscosity for martensitic phase transitions in shape memory alloys

In this paper, we investigate the decay rate of stabilization of the solution of the system of partial differential equations governing the dynamics of martensitic phase transitions in shape memory alloys under the presence of a viscous stress. The corresponding free energy is assumed in Landau-Ginzburg form and nonconvex as a function of the order parametr. We prove that for appropriate constants, which appear in the above-mentioned model, we can decide upon the exponencial decrease of the solution to its attractor for time tending to infinity

Stabilization of weak solutions of compressible Navier-Stokes equations for isothermal fluids with a nonlinear stress tensor

The aim of this paper is to study the stabilization of solutions to the Navier-Stokes equations for isothermal fluids with a nonlinear stress tensor. We study stabilization from the point of view of the method used in [17], where authors studied the asymptotic behaviour of solutions to barotropic compressible Navier-Stokes equations

Asymptotic analysis of elastic curved rods

We suppose a convergent sequence of curved rods made from an isotropic elastic material and clamped on the lower basis or on both bases, and the linearized elasticity system posed on the sequence of the curved rods. We study the asymptotic behaviour of the stress tensor and the solution to this system, when the radius of the domains tends to zero. The curved rods with a nonsmooth line of centroids are covered by the used asymptotic method as well

A general asymptotic model for Lipschitzian curved rods

In this paper we show that the asymptotic methods provide an advantageous approach to obtain models of thin elastic bodies under minimal regularity assumptions on the geometry. Our investigation is devoted to clamped curved rods with a nonsmooth line of centroids and the obtained model is a generalization of results already available in the literature

Relative energy inequality and weak-strong uniqueness for an isothermal non-Newtonian compressible fluid

Our paper deals with three-dimensional nonsteady Navier-Stokes equations for non-Newtonian compressible fluids. It contains a de­ri­va­tion of the relative energy inequality for the weak solutions to these equations. We show that the standard energy inequality implies the relative energy inequality. Consequently, the relative energy inequality allows us to achieve a weak-strong uniqueness result. In other words, we present that the weak solution of the Navier-Stokes system coincides with the strong solution emanated from the same initial conditions as long as the strong solution exists. For this purpose, a new assumption on the coercivity of the viscous stress tensor was introduced along with two natural examples satisfying it

DETERMINING ROAD NETWORK ROBUSTNESS AND PROPOSALS FOR ITS IMPROVEMENT

V příspěvku je aplikována metoda pro stanovení robustnosti sítě na dvě části silniční sítě Zlínského kraje. Dále je ukázáno, jak lze tuto metodu použít při návrhu nových spojení, které mají za cíl maximálně zvýšit jejich robustnost. Výsledkem výpočtů je návrh několika alternativ, jež mohou být k dispozici expertovi pro konečný výběr vhodného spojení.A method for measuring network robustness is applied to two parts of the Zlín region road network. We demonstrate how this method can be used to design new road links whose objective is a maximum increase in the entire network robustness. The computation results are several alternatives which should help experts make a final decision when choosing the most suitable link

A general asymptotic dynamic model for Lipschitzian elastic curved rods

We study the asymptotic behaviour of solutions to the linear evolution problem for clamped curved rods with the small thickness ε under minimal regularity assumptions on the geometry. In addition, nonconstant density of the curved rods is considered

Asymptotic analysis of elastic curved rods

We consider a sequence of curved rods which consist of isotropic material and which are clamped on the lower base or on both bases. We study the asymptotic behaviour of the stress tensor and displacement under the assumptions of linearized elasticity when the cross-sectional diameter of the rods tends to zero and the body force is given in the particular form. The analysis covers the case of a non-smooth limit line of centroids. We show how the body force and the choice of the approximating curved rods can affect the strong convergence and the limit form of the stress tensor for the curved rods clamped on both bases