Stability results of coupled wave models with locally memory in a past history framework via non smooth coefficients on the interface

Decay estimate in a viscoelastic plate equation with past history, nonlinear damping, and logarithmic nonlinearity

In this article, we consider a viscoelastic plate equation with past history, nonlinear damping, and logarithmic nonlinearity. We prove explicit and general decay rate results of the solution to the viscoelastic plate equation with past history. Convex properties, logarithmic inequalities, and generalised Young's inequality are mainly used to prove the decay estimate.

On the Stability of the Cauchy Problem of Timoshenko Thermoelastic Systems with Past History: Cattaneo and Fourier Law

In this paper, we investigate the decay properties of the thermoelastic Timoshenko system with past history in the whole space where the thermal effects are given by Cattaneo and Fourier laws. We obtain that both systems, Timoshenko-Fourier and Timoshenko-Cattaneo, have the same rate of decay $(1 + t)^{-1/8}$ and satisfy the regularity-loss type property. Moreover, for the Cattaneo case, we show that the decay rate depends of a new condition on the wave speed of propagation $χ_{0,τ}$. This new condition has been recently introduced to study the asymptotic behavior in bounded domains, see for i…

具有 past history 的耦合悬索桥系统的线性半群指数稳定性与全局吸引子

Exponential Stability of the Linear Semigroup and the Global Attractor for a Coupled Suspension Bridge System with Past History

本文针对具有 past history 的耦合悬索桥系统，结合Gearhart--Prüss定理等证明其线性半群指数稳定性，填补相关文献渐近光滑性证明的空白，得到自然能量空间中的紧全局吸引子。

具有过去历史和非局部边界阻尼的粘弹性梁方程的动力学

Dynamics for a viscoelastic beam equation with past history and nonlocal boundary dissipation

本文研究了具有过去历史和非局部边界阻尼的粘弹性梁方程的动力学，证明了其动力系统具有紧致全局吸引子和分形指数吸引子。

Overcoming the curse of dimensionality in the numerical approximation of Allen-Cahn partial differential equations via truncated full-history recursive multilevel Picard approximations

One of the most challenging problems in applied mathematics is the approximate solution of nonlinear partial differential equations (PDEs) in high dimensions. Standard deterministic approximation methods like finite differences or finite elements suffer from the curse of dimensionality in the sense that the computational effort grows exponentially in the dimension. In this work we overcome this difficulty in the case of reaction-diffusion type PDEs with a locally Lipschitz continuous coervice nonlinearity (such as Allen-Cahn PDEs) by introducing and analyzing truncated variants of the recently…