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Low regularity global solutions for nonlinear evolution equations of Kirchhoff type. (English) Zbl 1152.35077
The author establishes global-in-time existence results under very weak regularity requirements on the initial data. The consideration of low regularity solutions is quite natural in musical applications, where a typical initial configuration is the so-called plucked string, corresponding to a triangle shaped function. Thus the author considers the solutions below the regularity threshold which makes finite some positive functional conserved by time evolution.

MSC:
35L75 Higher-order nonlinear hyperbolic equations
35B40 Asymptotic behavior of solutions to PDEs
35B65 Smoothness and regularity of solutions to PDEs
35L70 Second-order nonlinear hyperbolic equations
74H30 Regularity of solutions of dynamical problems in solid mechanics
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