GLOBAL NONEXISTENCE FOR A VISCOELASTIC WAVE EQUATION WITH ACOUSTIC BOUNDARY CONDITIONS

doi:10.1007/s10473-020-0111-2

数学物理学报(英文版) ›› 2020, Vol. 40 ›› Issue (1): 155-169.doi: 10.1007/s10473-020-0111-2

GLOBAL NONEXISTENCE FOR A VISCOELASTIC WAVE EQUATION WITH ACOUSTIC BOUNDARY CONDITIONS

于佳利^1,2, 尚亚东², 狄华斐²

1. School of Science, Dalian Jiaotong University, Dalian 116028, China;
2. School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China

收稿日期:2018-11-07 修回日期:2019-05-09 出版日期:2020-02-25 发布日期:2020-04-14
通讯作者: Yadong SHANG E-mail:gzydshang@126.com
基金资助:
This work was supported by the NSF of China (11626070, 11801108), the Scientific Program of Guangdong Provience (2016A030310262), the College Scientific Research Project of Guangzhou City (1201630180), the Program for the Innovation Research Grant for the Postgraduates of Guangzhou University (2017GDJC-D08).

GLOBAL NONEXISTENCE FOR A VISCOELASTIC WAVE EQUATION WITH ACOUSTIC BOUNDARY CONDITIONS

Jiali YU^1,2, Yadong SHANG², Huafei DI²

1. School of Science, Dalian Jiaotong University, Dalian 116028, China;
2. School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China

Received:2018-11-07 Revised:2019-05-09 Online:2020-02-25 Published:2020-04-14
Contact: Yadong SHANG E-mail:gzydshang@126.com
Supported by:
This work was supported by the NSF of China (11626070, 11801108), the Scientific Program of Guangdong Provience (2016A030310262), the College Scientific Research Project of Guangzhou City (1201630180), the Program for the Innovation Research Grant for the Postgraduates of Guangzhou University (2017GDJC-D08).

摘要/Abstract

摘要： This paper deals with a class of nonlinear viscoelastic wave equation with damping and source terms
u_tt - △u - △u_t - △u_tt + ∫₀^tg(t - s)△u(s)ds + u_t|u_t|^m-2=u|u|^p-2
with acoustic boundary conditions. Under some appropriate assumption on relaxation function g and the initial data, we prove that the solution blows up in finite time if the positive initial energy satisfies a suitable condition.

关键词: viscoelastic wave equation, Global nonexistence, Acoustic boundary conditions

Abstract: This paper deals with a class of nonlinear viscoelastic wave equation with damping and source terms
u_tt - △u - △u_t - △u_tt + ∫₀^tg(t - s)△u(s)ds + u_t|u_t|^m-2=u|u|^p-2
with acoustic boundary conditions. Under some appropriate assumption on relaxation function g and the initial data, we prove that the solution blows up in finite time if the positive initial energy satisfies a suitable condition.

Key words: viscoelastic wave equation, Global nonexistence, Acoustic boundary conditions

中图分类号:

35L70

于佳利, 尚亚东, 狄华斐. GLOBAL NONEXISTENCE FOR A VISCOELASTIC WAVE EQUATION WITH ACOUSTIC BOUNDARY CONDITIONS[J]. 数学物理学报(英文版), 2020, 40(1): 155-169.

Jiali YU, Yadong SHANG, Huafei DI. GLOBAL NONEXISTENCE FOR A VISCOELASTIC WAVE EQUATION WITH ACOUSTIC BOUNDARY CONDITIONS[J]. Acta mathematica scientia,Series B, 2020, 40(1): 155-169.

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GLOBAL NONEXISTENCE FOR A VISCOELASTIC WAVE EQUATION WITH ACOUSTIC BOUNDARY CONDITIONS

GLOBAL NONEXISTENCE FOR A VISCOELASTIC WAVE EQUATION WITH ACOUSTIC BOUNDARY CONDITIONS

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