DYNAMIC PROPERTIES FOR NONLINEAR VISCOELASTIC KIRCHHOFF-TYPE EQUATION WITH ACOUSTIC CONTROL BOUNDARY CONDITIONS Ⅱ

Fushan Li; Shuai Xi; Ke Xu; Xiaomin Xue

doi:10.11948/20190085

2019 Volume 9 Issue 6

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Fushan Li, Shuai Xi, Ke Xu, Xiaomin Xue. DYNAMIC PROPERTIES FOR NONLINEAR VISCOELASTIC KIRCHHOFF-TYPE EQUATION WITH ACOUSTIC CONTROL BOUNDARY CONDITIONS Ⅱ[J]. Journal of Applied Analysis & Computation, 2019, 9(6): 2318-2332. doi: 10.11948/20190085

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Fushan Li, Shuai Xi, Ke Xu, Xiaomin Xue. DYNAMIC PROPERTIES FOR NONLINEAR VISCOELASTIC KIRCHHOFF-TYPE EQUATION WITH ACOUSTIC CONTROL BOUNDARY CONDITIONS Ⅱ[J]. Journal of Applied Analysis & Computation, 2019, 9(6): 2318-2332. doi: 10.11948/20190085

DYNAMIC PROPERTIES FOR NONLINEAR VISCOELASTIC KIRCHHOFF-TYPE EQUATION WITH ACOUSTIC CONTROL BOUNDARY CONDITIONS Ⅱ

1.
School of Mathematical Sciences, Qufu Normal University, Shandong 273165, China
2.
College of Mathematics and System Science, Shandong University of Science and Technology, Qingdao 266590, China

Corresponding author: Email address:fushan99@163.com(F. Li)
Fund Project: This work was supported by Natural Science Foundation of Shandong Province of China(ZR2019MA067)

Abstract

Abstract

In this paper, we consider the nonlinear viscoelastic Kirchhoff-type equation with initial conditions and acoustic boundary conditions. Under suitable conditions on the initial data, the relaxation function h(·) and M(·), we prove that the solution blows up in finite time and give the upper bound of the blow-up time T^*.
- Kirchhoff-type equation /
- acoustic boundary condition /
- blow-up
MSC: 35L05, 35L15, 35L70

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References

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