Chinese Quarterly Journal of Mathematics >

2025 , Vol. 40 >Issue 4: 417 - 440

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2025.04.008

Well-Posedness and Asymptotic Behavior of a Higher-Order Kirchhoff Equation#br#

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  • College of Science, China University of Petroleum, Qingdao 266580, China
ZHANG Liao (2000-), male, native of Heze, Shandong, master student of China University of Petroleum, engages in partial differential equations; LI Feng-jie (1974-), female, native of Yantai, Shandong, associate professor of China University of Petroleum, engages in partial differential equations.
LI Feng-jie (1974-), female, native of Yantai, Shandong, associate professor of China University of Petroleum, engages in partial differential equations.

Received date: 2025-06-13

  Online published: 2025-12-30

Supported by

Supported by Shandong Provincial Natural Science Foundation of China (Grant No. ZR2021MA003).

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Abstract

This paper focuses on the investigation of a hyperbolic Kirchhoff equation with nonlinear damping and higher-order dissipation terms. Initially, the existence and uniqueness of local weak solutions are rigorously established. Next, within the framework of potential well theory, the classification of solution behaviors, including blow-up and global existence, is systematically analyzed according to the relationships among the exponents of nonlinear source terms. Finally, explicit bounds for the blow-up time and decay estimates for global solutions are presented.

Key words： Higher-order dissipation; Kirchhoff equation; Blow-up; Blow-up time; Decay ; estimate

Cite this article

ZHANG Liao, LI Feng-jie . Well-Posedness and Asymptotic Behavior of a Higher-Order Kirchhoff Equation#br#[J]. Chinese Quarterly Journal of Mathematics, 2025 , 40(4) : 417 -440 . DOI: 10.13371/j.cnki.chin.q.j.m.2025.04.008

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