an:01422888
Zbl 0947.35020
Shibata, Yoshihiro
On the rate of decay of solutions to linear viscoelastic equation
EN
Math. Methods Appl. Sci. 23, No. 3, 203-226 (2000).
00062663
2000
j
35B40 74D05 35E15
Fourier analysis; Marcinkiewicz multiplier theorem; \(L^p-L^q\)-decay estimates
The author studies decay rates of solutions to the Cauchy problem for the equation of linear viscoelasticity in \(\mathbb{R}^n\): \(v_{tt} -\Delta v -\Delta v_t =0\). By using the Fourier analysis, the Marcinkiewicz multiplier theorem and careful estimating low- and high-frequency parts of the solutions, the author obtains the \(L^p-L^q\)-decay estimates (\(1\leq p\leq 2\leq q\leq\infty\)) of the solutions. The dominant asymptotic behavior is given by the convolution of Green functions of the diffusion equation and the wave equation. This paper improves some decay estimates in [\textit{D. Hoff} and \textit{K. Zumbrum}, Z. Angew. Math. Phys. 48, 597-614 (1997; Zbl 0882.76074)].
S.Jiang (Beijing)
Zbl 0882.76074