Blow-Up for a Stochastic Viscoelastic Lamé Equation with Logarithmic Nonlinearity

Abstract

In this paper, we consider an initial boundary value problem of stochastic viscoelastic wave equation with nonlinear damping and logarithmic nonlinear source terms. We proved a blow-up result for the solution with decreasing kernel.

Bilateral Harnack Inequalities for Stochastic Differential Equation with Multiplicative Noise

“…For b, σ, there exists an increasing function K on ½0, ∞Þ so that for all t ≥ 0, all y ′ , y ∈ ℝ d , and It follows from the above assumptions that the existence and uniqueness of the strong solution of SDE (1) are ensured (see Protter [1]). For more results about existence and uniqueness of the solution of differential equations, we can see [2][3][4].…”

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

“…Additionally, various authors, including those referenced as [1,4,5,9], have examined the blow-up problem within the framework of a Lame system. 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.…”