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

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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)

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.

Suggested Citation

  • Jum-Ran Kang & Hye-Jin Kim, 2025. "General Decay for a Viscoelastic Equation with Acoustic Boundary Conditions and a Logarithmic Nonlinearity," Mathematics, MDPI, vol. 13(16), pages 1-15, August.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:16:p:2684-:d:1728823
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