Well-posedness and exponential stability for the logarithmic Lamé system with a time delay

Blow-Up of Solution of Lamé Wave Equation with Fractional Damping and Logarithmic Nonlinearity Source Terms

“…The findings contributed valuable insights into the limitations and constraints of such equations, enriching our understanding of their dynamic behavior. In this scenario, Yüksekkaya et al [9], employing semigroup theory, addressed and established the well-posedness of an initial-boundary value problem for a logarithmic Lamé system with a time delay within a bounded domain. They further demonstrated the system's possession of global solutions using the well-depth method, subject to suitable assumptions on the weights of both the time delay and frictional damping.…”

Global existence and blow up of solution of wave nonlinear equation with boundary fractional damping and logarithmic source terms

“….., m. These functions satisfy (28)-(29) within a maximal interval [0, t m ), where 0 < t m ≤ T . Subsequently, we establish that t m = T and demonstrate that the local solution remains uniformly bounded, irrespective of m and t. To achieve this, we substitute u with w m t in (28) and perform integration by parts to obtain:…”

“…The significance of studying this specific system arises from its widespread applicability in diverse fields, such as potential problems [10]. In [28], the authors investigated the well-posedness and exponential stability of the logarithmic Lame system with a time delay. They focused on analyzing the mathematical properties and stability behavior of the system under these conditions.…”