Opuscula Math. 42, no. 2 (2022), 219-238
https://doi.org/10.7494/OpMath.2022.42.2.219
Opuscula Mathematica
Blowup phenomena for some fourth-order strain wave equations at arbitrary positive initial energy level
Abstract. In this paper, we study a series of fourth-order strain wave equations involving dissipative structure, which appears in elasto-plastic-microstructure models. By some differential inequalities, we derive the finite time blow up results and the estimates of the upper bound blowup time with arbitrary positive initial energy. We also discuss the influence mechanism of the linear weak damping and strong damping on blowup time, respectively.
Keywords: fourth-order strain wave equation, arbitrary positive initial energy, blowup, blowup time.
Mathematics Subject Classification: 35L05, 35A01, 35L55.
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- Qiang Lin
- College of Intelligent Systems Science and Engineering, Harbin Engineering University, Harbin 150001, P.R. China
- Yongbing Luo (corresponding author)
- College of Intelligent Systems Science and Engineering, Harbin Engineering University, Harbin 150001, P.R. China
- Communicated by Runzhang Xu.
- Received: 2021-08-12.
- Revised: 2022-01-25.
- Accepted: 2022-01-25.
- Published online: 2022-02-25.
