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Abstract: We consider the Timoshenko system in a bounded domain . The system has an indefinite damping mechanism, i.e. with a damping function possibly changing sign, present only in the equation for the rotation angle. We shall prove that the system is still exponentially stable under the same conditions as in the positive constant damping case, and provided and , for ϵ small enough. The decay rate will be described explicitly. In the arguments, we shall also give a new proof of exponential stability for the constant case . Moreover, we give a precise description of the decay rate and demonstrate that the system has the spectrum determined growth (SDG) property, i.e. the type of the induced semigroup coincides with the spectral bound for its generator. [Copyright &y& Elsevier]

Abstract: We consider the nonlinear wave equation in a bounded interval . The function is allowed to change sign, but has to satisfy . For this non-dissipative situation we prove the exponential stability of the corresponding linearized system for: (I) possibly large with small , and (II) a class of pairs with possibly negative moment . Estimates for the decay rate are also given in terms of . Moreover, we show the global existence of smooth, small solutions to the corresponding nonlinear system if, additionally, the negative part of is small enough. [Copyright &y& Elsevier]

Abstract: We consider initial–boundary value problems for the equations of isotropic elasticity for several mixed boundary conditions in infinite wave guides, as well as Maxwell equations. With the help of decompositions of the displacement field into divergence- and curl-free parts, respectively, which are compatible with the boundary conditions, we obtain sharp decay rates for the solutions. The decomposed systems correspond to the second-order Maxwell equations for the electric and the magnetic field with electric and magnetic boundary conditions, respectively. [Copyright &y& Elsevier]

We consider the Cauchy problem for a coupled system generalizing the thermoelastic plate equations. First we prove resolvent estimates for the stationary operator and conclude the analyticity of the associated semigroup in Lp-spaces, 1 < p < 1 ∞, for certain values of the parameters of the system; here the Newton polygon method is used. Then we prove decay rates of the Lq(ℝn)-norms of solutions, 2 ≥ q ≥ ∞, as time tends to infinity. [ABSTRACT FROM AUTHOR]

We investigate coupled systems of thermoelastic type in a general abstract form both modeling Fourier and Cattaneo type heat conduction. In particular we take into account a possible inertial term. A complete picture of the regions of exponential stability resp. non-exponential stability for the arising parameters (two from the type of thermoelastic system, one from the inertial term) is given. The regions of loss of exponential stability, while moving from the Fourier to the Cattaneo law, are thus clearly recognized and interestingly large. The polynomial stability in regions of non-exponential stability is also characterized. [ABSTRACT FROM AUTHOR]

For a class of bounded reference configurations that are of partially rectangular type, the linear system of magneto-elasticity in two space dimensions is considered and a polynomial decay rate of the energy as time tends to infinity is proved. [ABSTRACT FROM AUTHOR]