General decay and blow-up of solutions for a nonlinear wave equation with memory and fractional boundary damping terms

Abstract

The paper studies the global existence and general decay of solutions using Lyapunov functional for a nonlinear wave equation, taking into account the fractional derivative boundary condition and memory term. In addition, we establish the blow-up of solutions with nonpositive initial energy.

Asymptotic Behavior of Solutions to Free Boundary Problem with Tresca Boundary Conditions

“…With the help of these results, we will introduce some applications and provide some examples and some notes regarding weak contraction mappings. In addition, we will mention and give some results of the fixed point theory of weak contraction mappings by using the studied algorithm in ( [15,[22][23][24][25][26][27][28][29][30][31][32][33][34][35]).…”

A New Result of Stability for Thermoelastic-Bresse System of Second Sound Related with Forcing, Delay, and Past History Terms

“…The Bresse system ( 10) is more general than the wellknown Timoshenko system where the longitudinal displacement ω is not considered l = 0. The reader may refer to, for example, [24][25][26][27][28][29][30][31][32][33][34].…”

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

“…The study aimed to understand the long-term behavior of the system under fractional boundary damping conditions. In [11], the behavior of solutions for a nonlinear wave equation with memory and fractional boundary damping terms was studied, examining both general decay and the potential for solution blow-up. The study aimed to elucidate the impact of memory and fractional damping on the long-term dynamics of the system.…”

“…Next, considering the conditions specified in Lemma 3.2 for part (i), and taking into account (18) and (11), it becomes evident that:…”