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In this paper, we consider a viscoelastic plate equation with a logarithmic nonlinearity. Using the Galaerkin method and the multiplier method, we establish the existence of solutions and prove an explicit and general decay rate result. This result extends and improves many results in the literature such as Gorka [19], Hiramatsu et al. [27] and Han and Wang [26].

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In this paper, we consider the following dissipative viscoelastic with memorytype Timoshenko systemwith Dirichlet boundary conditions, where g is a positive non-increasing function satisfying, for some nonnegative functions ξ and H,Under appropriate conditions on ξ and H, we establish some new decay results for the case of equal-speeds of propagation that generalize and improve many earlier results in the literature.

In this paper, we consider a viscoelastic plate equation with a velocity-dependent material density and a logarithmic nonlinearity. Using the Faedo-Galaerkin approximations and the multiplier method, we establish the existence of the solutions of the problem and we prove an explicit and general decay rate result. These results extend and improve many results in the literature.

In this paper, we investigate the stability of the solutions of a viscoelastic plate equation with a logarithmic nonlinearity. We assume that the relaxation function g satisfies the minimal condition g (t) ≤-ξ (t)G(g(t)), where ξ and G satisfy some properties. With this very general assumption on the behavior of g, we establish explicit and general energy decay results from which we can recover the exponential and polynomial rates when G(s) = s p and p covers the full admissible range [1, 2). Our new results substantially improve and generalize several earlier related results in the literature such as Gorka (

In this paper, we consider the following viscoelastic problem with variable exponent nonlinearities:where m(.) and q(.) are two functions satisfying specific conditions. This type of problems appears in fluid dynamics, the electrorheological fluids (smart fluids), which show changing (often dramatically) in the viscosity when an electrical field is applied. The Lebesgue and Sobolev spaces with variable exponents are efficient tools to analyze such problems. In this work, we prove a global existence result using the well-depth method and establish explicit and general decay results under a very general assumption on the relaxation function. Our results extend and generalize many results in the literature.