General Decay for a Viscoelastic Equation with Acoustic Boundary Conditions and a Logarithmic Nonlinearity

Jum-Ran Kang and Hye-Jin Kim ()
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Jum-Ran Kang: Department of Applied Mathematics, Pukyong National University, Busan 48513, Republic of Korea
Hye-Jin Kim: Department of Applied Mathematics, Pukyong National University, Busan 48513, Republic of Korea

Mathematics, 2025, vol. 13, issue 16, 1-15

Abstract: In this work, we investigate the stability of solutions in a situation where the logarithmic source term competes with the viscoelastic dissipation under acoustic boundary conditions. We assume minimal conditions on the relaxation function g , namely, g ′ ( t ) ≤ − ξ ( t ) H ( g ( t ) ) , where H is a strictly increasing and strictly convex function near the origin, and ξ ( t ) is a non-increasing function. Under these general assumptions, we establish a general decay estimate for the solution. This result extends and improves some previous results.

Keywords: viscoelastic equation; logarithmic nonlinearity; general decay; acoustic boundary conditions; convexity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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