Global existence, general decay and blow-up for a nonlinear wave equation with logarithmic source term and fractional boundary dissipation

Abstract

<p style='text-indent:20px;'>In this paper, we consider a wave equation with logarithmic source term and fractional boundary dissipation. We study the global existence of the solution under some conditions and prove the general decay of the solution in this case by using the Lyapunov functional. Also, the blow-up of solution is established at three different levels of energy using the potential well method.</p>

Classical Solutions of a Mixed Problem with the Zaremba Boundary Condition for a Mildly Quasilinear Wave Equation

“…(1.1) is well developed. Various methods are used to study these problems: the Galerkin method [13], the energy methods [14,15,16], the theory of potential well [17,18,19], the Leray-Schauder degree theory [20], representations of solutions in the form of series [21], the test function method [22], collocation methods [23], topological methods [24,25]. However, these works mainly study generalized solutions rather than ones.…”

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

“…Here, b is a nonnegative real number, and ∂ α,η t represents Caputo's generalized fractional derivative with 0 < α < 1. This derivative is defined in [2,3] as given below:…”

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

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