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Zbl 1172.35504
Zhou, Yong
Blow-up of solutions to a nonlinear dispersive rod equation. (English)
[J] Calc. Var. Partial Differ. Equ. 25, No. 1, 63-77 (2006). ISSN 0944-2669; ISSN 1432-0835/e

Summary: In this paper, firstly we find the best constant for a convolution problem on the unit circle via a variational method. Then we apply the best constant on a nonlinear rod equation to give sufficient conditions on the initial data, which guarantee finite time singularity formation for the corresponding solutions.
MSC 2000:
*35Q72 Other PDE from mechanics
35B40 Asymptotic behavior of solutions of PDE
35G25 Initial value problems for nonlinear higher-order PDE
74B20 Nonlinear elasticity
74H20 Existence of solutions
74K10 Rods (beams, columns, shafts, arches, rings, etc.)

Keywords: Best constant; Convolution problem; Rod equation; Singularity

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