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449
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...
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...
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...
The asymptotic behaviour for 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...
We prove -regularity for the stresses in the Prandtl-Reuss-law. The proof runs via uniform estimates for the Norton-Hoff-approximation.
The nonlinear integro-differential system associated with the penetration of a magnetic field into a substance is considered. The asymptotic behavior as 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...
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.
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 . Moreover, we assume that the stored energy function is with respect to x and . In our description we assume that Piola-Kirchhoff’s stress tensor depends on the tensor . This means...
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...
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...
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449