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This article explores blow-up phenomena in nonlinear logarithmic wave equations with fractional damping, infinite memory, and strong dissipation. The paper proves the existence of a local weak solution using semigroup theory. Furthermore, this research demonstrates that under certain conditions in finite time, the local solution may blow-up by using an appropriate Lyapunov functional. The findings highlight the effectiveness of strong damping, particularly when combined with fractional damping. [ABSTRACT FROM AUTHOR]

We investigate a variable-coefficient wave equation with interior local frictional damping and memory-type dynamic boundary conditions. The innovation of the paper lies in the presence of dynamic boundary conditions, thus we need some special techniques to deal with the high-order terms on the boundary. By the Riemannian geometry method and the multiplier technique, we establish the stable results, and the energy decay result of system is described by employing the solution of a stable first-order ordinary differential equation. The stability depends on the frictional damping function and kernel function, thereby improving and generalizing the results of prior references. [ABSTRACT FROM AUTHOR]

In this paper, we consider a variable coefficient viscoelastic semilinear wave equation with logarithmic source term and acoustic boundary conditions in domains with non‐locally reacting boundary. By potential well method, we get the global existence of solution and through several important lemmas, we prove the general energy decay estimate of the system. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the general stability results of a fully dynamic piezoelectric beam system with internal fractional delays under memory boundary controls. Firstly, by introducing two new equations and using two Volterra's inverse operators to deal with fractional delay terms and boundary memory terms, respectively, a new equivalent system is obtained. Secondly, by combining Faedo–Galerkin approximations with the compactness argument, we prove the local existence and uniqueness of weak solution. Finally, under a broader class of kernel functions, by constructing Lyapunov functionals and new equations and applying some technical lemmas, we establish the optimal and explicit energy decay results for two cases, namely, initial values (v0,p0)=(0,0)$$ \left({v}_0,{p}_0\right)=\left(0,0\right) $$ and without imposing initial values equal to 0, that is, (v0,p0)≠(0,0)$$ \left({v}_0,{p}_0\right)\ne \left(0,0\right) $$. It is worth pointing out that we focus more on the analysis of (v0,p0)≠(0,0)$$ \left({v}_0,{p}_0\right)\ne \left(0,0\right) $$, because the stability results of (v0,p0)=(0,0)$$ \left({v}_0,{p}_0\right)=\left(0,0\right) $$ are special cases of (v0,p0)≠(0,0)$$ \left({v}_0,{p}_0\right)\ne \left(0,0\right) $$. This is the first time to analyze the stability of strong coupling problem by combining internal fractional delay and boundary viscoelastic damping. The obtained general decay results are not necessarily exponential or polynomial, which generalize the relevant results in the existing literature. [ABSTRACT FROM AUTHOR]

In this paper, we consider a multi-dimensional wave equation with delay and dynamic boundary conditions, related to the Kelvin–Voigt damping. By using the Faedo–Galerkin approximations together with some priori estimates, we prove the local existence of solution. Since the damping may stabilize the system while the delay may destabilize it, we discuss the interaction between the damping and the delay, and obtain that the system is uniformly stable when the effect of damping is greater than that of time delay. Exponential stability result of system is also established by constructing suitable Lyapunov functionals. [ABSTRACT FROM AUTHOR]

In this paper, we consider a quasilinear viscoelastic wave equation that features a distributed delay as well as logarithmic nonlinearity. We combine the potential well theory, Faedo‐Galerkin's approximation, and some energy estimates to construct the global existence of the solution. With weaker conditions on the relaxation function, we establish explicit and general decay rate results by using the multiplier method and some properties of convex functions. Our results improve and generalize several earlier related results in the literature. [ABSTRACT FROM AUTHOR]

In this paper we consider a system of viscoelastic wave equations of Kirchhoff type with dynamic boundary conditions. Supposing the relaxation functions $ g_i $ $ (i = 1, 2, \cdots, l) $ satisfy $ g_i(t)\leq-\xi_i(t)G(g_i(t)) $ where $ G $ is an increasing and convex function near the origin and $ \xi_i $ are nonincreasing, we establish some optimal and general decay rates of the energy using the multiplier method and some properties of convex functions. Moreover, we obtain the finite time blow-up result of solution with nonpositive or arbitrary positive initial energy. The results in this paper are obtained without imposing any growth condition on weak damping term at the origin. Our results improve and generalize several earlier related results in the literature. [ABSTRACT FROM AUTHOR]