Initial value problem for a class of fourth-order nonlinear wave equations
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In this paper, existence and uniqueness of the generalized global solution and the classical global solution to the initial value problem for a class of fourth-order nonlinear wave equations are studied in the fractional order Sobolev space using the contraction mapping principle and the extension theorem. The sufficient conditions for the blow up of the solution to the initial value problem are given.
Key wordsfourth-order nonlinear wave equation initial value problem global solution blow up of solution
Chinese Library ClassificationO175.29 O175.27
2000 Mathematics Subject Classification35L30 35G25
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- Zhu, Weiqui. Nonlinear waves in elastic rods (in Chinese). Acta Mechanica Solida Sinica 1(2): 247–253 (1980)Google Scholar