Volume 1 • Issue 1 • PP: 47-55 • 2023
The Decay of The Solutions of a Nonlinear Viscoelastic Hyperbolic Equation
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We study under some conditions on p, m and suitable conditions on g, the decay of solutions of the nonlinear viscoelastic hyperbolic equation in problem (P) as t→+∞, with Ω is a bounded domain in R^N (N>1), with smooth boundary Γ, and a, b, w are positive constants, m≥2, P≥2, and the function g(t) satisfying some conditions. We show that the energy of solutions decays exponentially if m =2 and polynomial if m >2, provided that the initial data are small enough.
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References
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