669 research outputs found
Exponential energy decay of solutions for a system of viscoelastic wave equations of Kirchhoff type with strong damping
The initial boundary value problem for a system of viscoelastic wave
equations of Kirchhoff type with strong damping is considered. We prove that,
under suitable assumptions on relaxation functions and certain initial data,
the decay rate of the solutions energy is exponential
Global nonexistence of solutions for the viscoelastic wave equation of Kirchhoff type with high energy
In this paper we consider the viscoelastic wave equation of Kirchhoff type:
with Dirichlet boundary conditions. Under some suitable
assumptions on and the initial data, we established a global nonexistence
result for certain solutions with arbitrarily high energy.Comment: 12 page
Dynamics of thermoelastic thin plates: A comparison of four theories
Four distinct theories describing the flexural motion of thermoelastic thin
plates are compared. The theories are due to Chadwick, Lagnese and Lions,
Simmonds, and Norris. Chadwick's theory requires a 3D spatial equation for the
temperature but is considered the most accurate as the others are derivable
from it by different approximations. Attention is given to the damping of
flexural waves. Analytical and quantitative comparisons indicate that the
Lagnese and Lions model with a 2D temperature equation captures the essential
features of the thermoelastic damping, but contains systematic inaccuracies.
These are attributable to the approximation for the first moment of the
temperature used in deriving the Lagnese and Lions equation. Simmonds' model
with an explicit formula for temperature in terms of plate deflection is the
simplest of all but is accurate only at low frequency, where the damping is
linearly proportional to the frequency. It is shown that the Norris model,
which is almost as simple as Simmond's, is as accurate as the more precise but
involved theory of Chadwick.Comment: 2 figures, 1 tabl
EXPONENTIAL GROWTH OF SOLUTIONS FOR A VARIABLE-EXPONENT FOURTH-ORDER VISCOELASTIC EQUATION WITH NONLINEAR BOUNDARY FEEDBACK
In this paper we study a variable-exponent fourth-order viscoelastic equation of the formin a bounded domain of . Under suitable conditions on variable exponents and initial data, we prove that the solutions will grow up as an exponential function with positive initial energy level. Our result improves and extends many earlier results in the literature such as the on by Mahdi and Hakem (Ser. Math. Inform. 2020, https://doi.org/10.22190/FUMI2003647M)
EXPONENTIAL DECAY OF WAVE EQUATION WITH A VISCOELASTIC BOUNDARY CONDITION AND SOURCE TERM
In this paper we are concerned with the stability of solutions for the wave equation with a viscoelastic Boundary condition and source term by using the potential well method, the multiplier technique and unique continuation theorem for the wave equation with variable coefficient
On a Nonlinear Degenerate Evolution Equation with Nonlinear Boundary Damping
This paper deals essentially with a nonlinear degenerate evolution equation of the form Ku″-Δu+∑j=1nbj∂u′/∂xj+uσu=0 supplemented with nonlinear boundary conditions of Neumann type given by ∂u/∂ν+h·, u′=0. Under suitable conditions the existence and uniqueness of solutions are shown and that the boundary damping produces a uniform global stability of the corresponding solutions
Global Solution and Asymptotic Behaviour for a Wave Equation Type p-Laplacian with p-Laplacian Damping
In this work we study the global solution, uniqueness and asymptotic behaviour of the nonlinear equation
utt − ∆pu − ∆put =|u|r−1u
where ∆pu is the nonlinear p-Laplacian operator, 2 ≤ p < ∞. The global solutions are constructed by means of the Faedo-Galerkin approximations and the asymptotic behavior is obtained by Nakao method. Keywords: p-Laplacian, global solution, asymptotic behaviour, p-Laplacian damping
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