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Blowup phenomena for some fourth-order strain wave equations at arbitrary positive initial energy level

Lin Qiang, Luo Yongbing

Opuscula Mathematica

2022

Vol. 42, no. 2

219--238

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.

Smooth blowup square for motives with modulus

Kelly Shane, Saito Shuji

Bulletin of the Polish Academy of Sciences. Mathematics

2021

Vol. 69, no. 2

97--106

In this self-contained paper we prove that Voevodsky’s smooth blowup triangle of motives generalises to a smooth blowup triangle of motives with modulus.

On nonexistence of global in time solution for a mixed problem for a nonlinear evolution equation with memory generalizing the Voigt-Kelvin rheological model

Pukach P., Il'kiv V., Nytrebych Z., Vovk M.

Opuscula Mathematica

2017

Vol. 37, no. 5

735--753

The paper deals with investigating of the first mixed problem for a fifth-order nonlinear evolutional equation which generalizes well known equation of the vibrations theory. We obtain sufficient conditions of nonexistence of a global solution in time variable.