In this paper a procedure for construction of complete type Lyapunov–Krasovskii functionals for a scalar neutral type time delay equation is considered. The construction of the functionals depends on the so-called Lyapunov functions which satisfy a delay equation with additional boundary conditions. It is shown that these functionals admit lower and upper quadratic bounds. Exponential estimates...

Many rubber like materials present a stress-softening phenomenon known as Mullins effect. It is characterized by a difference of behavior between the first and second loading and by a residual strain after a first loading. Moreover according to the literature this stress softening is anisotropic. A new constitutive equation is proposed. It relies on the decomposition of the macromolecular netwo...

We investigate the well-posedness, the exponential stability, or the lack thereof, of thermoelastic systems in materials where, in contrast to classical thermoelastic models for Kirchhoff type plates, two temperatures are involved, related by an elliptic equation. The arising initial boundary value problems for different boundary conditions deal with systems of partial differential equations in...

Abstract. We consider the Stokes-Oldroyd equations, defined here as the Stokes equations with the Newtonian constitutive equation explicitly included. Thus a polymer-like stress tensor is included so that the dependent variable structure of a viscoelastic model is in place. The energy equation is coupled with the mass, momentum, and constitutive equations through the use of temperature-dependen...

In order to describe the deformation properties due to the martensitic transformation and the R-phase transformation of TiNi shape memory alloy, a thermomechanical constitutive equation considering the volume fractions of induced phases associated with both transformations is developed. The proposed constitutive equation expresses well the properties of the shape memory effect, pseudoelasticity...

In this paper, the exp-function method is improved to construct exact solutions of non-linear lattice equations by modifying its exponential function ansätz. The improved method has two advantages. One is that it can solve non-linear lattice equations with variable coefficients, and the other is that it is not necessary to balance the highest order derivative with the highest order nonlinear te...

water quality prediction is a valuable tool for pollutant control in aquatic environments. a river system is selected and one-dimensional flow is assumed for the simulation of pollutant transport in this paper. advective and diffusive terms of transport equation are considered separately. different functions of advective transport are proposed and applied for a specified velocity on the discret...

In this article we consider the numerical approximation to the time dependent viscoelasticity equations with an Oldroyd B constitutive equation. The approximation is stabilized by using a SUPG approximation for the constitutive equation. We analyse both the semi-discrete and fully discrete numerical approximations. For both discretizations we prove the existence of, and derive a priori error es...

This note studies the linearly damped generalized Hartree equation iu˙−(−Δ)su+iau=±|u|p−2(Jγ∗|u|p)u,0<s<1,a>0,p≥2. Indeed, one proves an exponential scattering of energy global solutions, with spherically symmetric datum. means that, for large time, solution goes exponentially to associated free problem iu˙−(−Δ)su+iau=0, in Hs norm. The radial assumption avoids a loss regularity Strich...

This paper deals with the initial boundary value problem of Petrovsky type equation degenerate damping. Under some appropriate conditions, we study finite time blow up and exponential growth solutions negative energy.