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$H^{s}$-global well-posedness for semilinear wave equations. (English) Zbl 1024.35079
The authors derive a priori estimates for semilinear wave equation $u_{tt}-\triangle u=-|u|^{p-1}u$, $(t,x\in \bbfR\times \bbfR^n$, $n\geq 3)$ in order to prove existence and uniqueness of global solution to the Cauchy problem for the equation.

MSC:
35L70Nonlinear second-order hyperbolic equations
35L15Second order hyperbolic equations, initial value problems
35B40Asymptotic behavior of solutions of PDE
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References:
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