Stability of initial-boundary value problem for quasilinear viscoelastic equations
| dc.contributor.author | Jin, Kun-Peng | |
| dc.contributor.author | Liang, Jin | |
| dc.contributor.author | Xiao, Ti-Jun | |
| dc.date.accessioned | 2021-10-04T16:39:41Z | |
| dc.date.available | 2021-10-04T16:39:41Z | |
| dc.date.issued | 2020-07-30 | |
| dc.description.abstract | We investigate the stability of the initial-boundary value problem for the quasilinear viscoelastic equation |ut|ρutt - ∆utt - ∆u + ∫t0 g(t - s)∆u(s)ds = 0, in Ω x (0, +∞), u = 0, in ∂Ω x (0, +∞), u(‧, 0) = u0(x), ut(‧, 0) = u1(x), in Ω, where Ω is a bounded domain in ℝn (n ≥ 1) with smooth boundary ∂Ω, ρ is a positive real number, and g(t) is the relaxation function. We present a general polynomial decay result under some weak conditions on g, which generalizes and improves the existing related results. Moreover, under the condition g′(t) ≤ −ξ(t)gp(t), we obtain uniform exponential and polynomial decay rates for 1 ≤ p < 2, while in the previous literature only the case 1 ≤ p < 3/2 was studied. Finally, under a general condition g′(t) ≤ -H(g(t)), we establish a fine decay estimate, which is stronger than the previous results. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 15 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Jin, K. P., Liang, J., & Xiao, T. J. (2020). Stability of initial-boundary value problem for quasilinear viscoelastic equations. <i>Electronic Journal of Differential Equations, 2020</i>(85), pp. 1-15. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/14592 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2020, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | Quasilinear viscoelastic equation | |
| dc.subject | Polynomial and exponential decay | |
| dc.subject | Relaxation function | |
| dc.subject | Uniform decay | |
| dc.title | Stability of initial-boundary value problem for quasilinear viscoelastic equations | |
| dc.type | Article |