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- W327325918 abstract "Semilinear abstract second order equation with a memory is considered. The memory kernel g(t) is subject to a general assumption, introduced for the first time in Alabau-Boussouira and Cannarsa (C. R. Acad. Sci. Paris Ser. I 347, 867–872, 2009), g′ ≤ −H(g), where the function $$H(cdot ) in C^{1}(R^{+})$$ is positive, increasing and convex with H(0) = 0. The corresponding result announced in Alabau-Boussouira and Cannarsa (C. R. Acad. Sci. Paris Ser. I 347, 867–872, 2009) (with a brief idea about the proof) provides the decay rates expressed in terms of the relaxation kernel in the case relaxation kernel satisfies the equality $$g' = -H(g)$$ (Theorem 2.2 in Alabau-Boussouira and Cannarsa, C. R. Acad. Sci. Paris Ser. I 347, 867–872, 2009). In the case of inequality g′ ≤ −H(g), Alabau-Boussouira and Cannarsa (C. R. Acad. Sci. Paris Ser. I 347, 867–872, 2009) claims uniform decay of the energy without specifying the rate (Theorem 2.1 in Alabau-Boussouira and Cannarsa, C. R. Acad. Sci. Paris Ser. I 347, 867–872, 2009). The result presented in this paper establishes the decay rate estimates for the general case of inequality g′ ≤−H(g). The decay rates are expressed (Theorem 2 ) in terms of the solution to a given nonlinear dissipative ODE governed by H(s). Applications to semilinear elasto-dynamic systems with memory are also provided." @default.
- W327325918 created "2016-06-24" @default.
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- W327325918 date "2014-01-01" @default.
- W327325918 modified "2023-10-17" @default.
- W327325918 title "Intrinsic Decay Rate Estimates for Semilinear Abstract Second Order Equations with Memory" @default.
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- W327325918 doi "https://doi.org/10.1007/978-3-319-11406-4_14" @default.
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