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Blow-up of solutions to a nonlinear dispersive rod equation. (English) Zbl 1172.35504
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.

35Q72Other PDE from mechanics (MSC2000)
35B40Asymptotic behavior of solutions of PDE
35G25Initial value problems for nonlinear higher-order PDE
74B20Nonlinear elasticity
74H20Existence of solutions for dynamical problems in solid mechanics
74K10Rods (beams, columns, shafts, arches, rings, etc.) in solid mechanics
Full Text: DOI
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