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In this paper we consider a system of Timoshenko-thermoelasticity with second sound in the presence of an infinite history term. We prove, under suitable conditions on the coefficients and the relaxation function, a general decay result from which the exponential and polynomial decay estimates are only special cases. We also establish a lack of exponential decay result and discuss the optimality for some situation. [ABSTRACT FROM AUTHOR]

In this paper, we consider a plate equation with a logarithmic nonlinearity in the presence of a frictional damping. We prove, for a suitably chosen initial data, a global existence as well as a decay result. [ABSTRACT FROM AUTHOR]

Abstract: This work is concerned with a system of viscoelastic wave equations with nonlinear damping and source terms acting in both equations. We prove a global nonexistence theorem for certain solutions with positive initial energy. [Copyright &y& Elsevier]

Abstract: Fernández Sare and Rivera [H.D. Fernández Sare, J.E. Muñoz Rivera, Stability of Timoshenko systems with past history, J. Math. Anal. Appl. 339 (1) (2008) 482–502] considered the following Timoshenko-type system where g is a positive differentiable exponentially decaying function. They established an exponential decay result in the case of equal wave-speed propagation and a polynomial decay result in the case of nonequal wave-speed propagation. In this paper, we study the same system, for g decaying polynomially, and prove polynomial stability results for the equal and nonequal wave-speed propagation. Our results are established under conditions on the relaxation function weaker than those in [H.D. Fernández Sare, J.E. Muñoz Rivera, Stability of Timoshenko systems with past history, J. Math. Anal. Appl. 339 (1) (2008) 482–502]. [Copyright &y& Elsevier]

Abstract: In this paper we consider a one-dimensional linear thermoelastic system of Timoshenko type, where the heat conduction is given by Green and Naghdi theories. We prove the exponential stability by using the energy method. [Copyright &y& Elsevier]

Abstract: In this paper we consider the following viscoelastic equation: in a bounded domain, and establish a general decay result which is not necessarily of exponential or polynomial type. This work generalizes and improves earlier results in the literature. [Copyright &y& Elsevier]

Abstract: In this paper, we consider the nonlinear viscoelastic equation with initial conditions and Dirichlet boundary conditions. For nonincreasing positive functions g and for , we prove that there are solutions with positive initial energy that blow up in finite time. [Copyright &y& Elsevier]

In this work we consider an initial boundary value problem related to the equation ut−div&z.sfnc;∇u&z.sfnc;m−2∇u=f(u) and prove, under suitable conditions on f, a blow up result for solutions with vanishing or negative initial energy. [Copyright &y& Elsevier]

In this paper we consider the nonlinearly damped semilinear Petrovsky equationutt + Δ2u + aut&z.sfnc;ut&z.sfnc;m − 2 = bu&z.sfnc;u&z.sfnc;p − 2in a bounded domain, where a, b > 0. We prove the existence of a local weak solution and show that this solution blows up in finite time if p > m and the energy is negative. We also show that the solution is global if m ≥ p. [Copyright &y& Elsevier]

Feng and Apalara (2019) [16] investigated the one-dimensional porous-elastic system with finite memory under the assumptions of equal-speed wave propagations and positive definite energy associated with the solution, and established an optimal explicit energy decay rate. In this paper, we consider the case of non-equal wave speeds and positive semidefinite energy, which are more realistic from the physics point of view. By using the second-order energy, we prove some new decay results that generalize and improve many earlier results in the literature. [ABSTRACT FROM AUTHOR]