This paper is concerned with the energy decay for a class of plate equations with memory and lower order perturbation of p-Laplacian type,with simply supported boundary condition, where is a bounded domain of R N , g > 0 is a memory kernel that decays exponentially and f .u/ is a nonlinear perturbation. This kind of problem without the memory term models elastoplastic flows.A more general equation,

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This paper is concerned with asymptotic stability of a Bresse system with two frictional dissipations. Under mathematical condition of equal speed of wave propagation, we prove that the system is exponentially stable. Otherwise, we show that Bresse system is not exponentially stable. Then, in the latter case, by using a recent result in linear operator theory, we prove the solution decays polynomially to zero with optimal decay rate. Better rates of polynomial decay depending on the regularity of initial data are also achieved. Copyright © 2014 John Wiley & Sons, Ltd.

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Articles you may be interested inLong-time behavior of a two-layer model of baroclinic quasi-geostrophic turbulence Statistics of return times in a self-similar model Chaos 9, 715 (1999); This paper is concerned with a class of Kirchhoff models with memory effects u ttdefined in a bounded domain of R N . This non-autonomous equation corresponds to a viscoelastic version of Kirchhoff models arising in dynamics of elastoplastic flows and plate vibrations. Under assumptions that the exponent p and the growth of f(u) are up to the critical range, it turns out that the model corresponds to an autonomous dynamical system in a larger phase space, by adding a component which describes the relative displacement history. Then the existence of a global attractor is granted. Furthermore, in the subcritical case, this global attractor has finite Hausdorff and fractal dimensions. C 2013 American Institute of Physics. [http://dx.