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Approximation of the vibration modes of a plate coupled with a fluid by low-order isoparametric finite elements

Erwin Hernández (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We analyze an isoparametric finite element method to compute the vibration modes of a plate, modeled by Reissner-Mindlin equations, in contact with a compressible fluid, described in terms of displacement variables. To avoid locking in the plate, we consider a low-order method of the so called MITC (Mixed Interpolation of Tensorial Component) family on quadrilateral meshes. To avoid spurious modes in the fluid, we use a low-order hexahedral Raviart-Thomas elements and a non conforming coupling...

Asymptotic behavior of the numerical solutions of time-delayed reaction diffusion equations with non-monotone reaction term

Yuan-Ming Wang (2003)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

This paper is concerned with the asymptotic behavior of the finite difference solutions of a class of nonlinear reaction diffusion equations with time delay. By introducing a pair of coupled upper and lower solutions, an existence result of the solution is given and an attractor of the solution is obtained without monotonicity assumptions on the nonlinear reaction function. This attractor is a sector between two coupled quasi-solutions of the corresponding “steady-state” problem, which are obtained...

Asymptotic behavior of the numerical solutions of time-delayed reaction diffusion equations with non-monotone reaction term

Yuan-Ming Wang (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

This paper is concerned with the asymptotic behavior of the finite difference solutions of a class of nonlinear reaction diffusion equations with time delay. By introducing a pair of coupled upper and lower solutions, an existence result of the solution is given and an attractor of the solution is obtained without monotonicity assumptions on the nonlinear reaction function. This attractor is a sector between two coupled quasi-solutions of the corresponding “steady-state" problem, which are...

Asymptotic behaviour for a phase-field model with hysteresis in one-dimensional thermo-visco-plasticity

Olaf Klein (2004)

Applications of Mathematics

The asymptotic behaviour for t → ∞ of the solutions to a one-dimensional model for thermo-visco-plastic behaviour is investigated in this paper. The model consists of a coupled system of nonlinear partial differential equations, representing the equation of motion, the balance of the internal energy, and a phase evolution equation, determining the evolution of a phase variable. The phase evolution equation can be used to deal with relaxation processes. Rate-independent hysteresis effects in the strain-stress...

Asymptotics for large time of solutions to nonlinear system associated with the penetration of a magnetic field into a substance

Temur A. Jangveladze, Zurab V. Kiguradze (2010)

Applications of Mathematics

The nonlinear integro-differential system associated with the penetration of a magnetic field into a substance is considered. The asymptotic behavior as t → ∞ of solutions for two initial-boundary value problems are studied. The problem with non-zero conditions on one side of the lateral boundary is discussed. The problem with homogeneous boundary conditions is studied too. The rates of convergence are given. Results presented show the difference between stabilization characters of solutions of these...

Bifurcation theory of the time-dependent von Kármán equations

Igor Brilla (1984)

Aplikace matematiky

In this paper the author studies existence and bifurcation of a nonlinear homogeneous Volterra integral equation, which is derived as the first approximation for the solution of the time dependent generalization of the von Kármán equations. The last system serves as a model for stability (instability) of a thin rectangular visco-elastic plate whose two opposite edges are subjected to a constant loading which depends on the parameters of proportionality of this boundary loading.

Blow-up of the solution to the initial-value problem in nonlinear three-dimensional hyperelasticity

J. A. Gawinecki, P. Kacprzyk (2008)

Applicationes Mathematicae

We consider the initial value problem for the nonlinear partial differential equations describing the motion of an inhomogeneous and anisotropic hyperelastic medium. We assume that the stored energy function of the hyperelastic material is a function of the point x and the nonlinear Green-St. Venant strain tensor e j k . Moreover, we assume that the stored energy function is C ∞ with respect to x and e j k . In our description we assume that Piola-Kirchhoff’s stress tensor p j k depends on the tensor e j k . This means...

Boundary feedback stabilization of a three-layer sandwich beam : Riesz basis approach

Jun-Min Wang, Bao-Zhu Guo, Boumediène Chentouf (2006)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper, we consider the boundary stabilization of a sandwich beam which consists of two outer stiff layers and a compliant middle layer. Using Riesz basis approach, we show that there is a sequence of generalized eigenfunctions, which forms a Riesz basis in the state space. As a consequence, the spectrum-determined growth condition as well as the exponential stability of the closed-loop system are concluded. Finally, the well-posedness and regularity in the sense of Salamon-Weiss class as...

Boundary feedback stabilization of a three-layer sandwich beam: Riesz basis approach

Jun-Min Wang, Bao-Zhu Guo, Boumediène Chentouf (2005)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper, we consider the boundary stabilization of a sandwich beam which consists of two outer stiff layers and a compliant middle layer. Using Riesz basis approach, we show that there is a sequence of generalized eigenfunctions, which forms a Riesz basis in the state space. As a consequence, the spectrum-determined growth condition as well as the exponential stability of the closed-loop system are concluded. Finally, the well-posedness and regularity in the sense of Salamon-Weiss class as...

Currently displaying 81 – 100 of 449