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Nonlinear wave equation with potential. (English) Zbl 0979.35103

The author proves the existence of a unique global solution of the Cauchy problem for the equation \(u_{tt}-\triangle u+V(x)|u|^{p-1}u=0\) \((x\in \mathbb{R}^{n}\), \(t>0)\), where \(V(x)=|x-x_{0}|\) for \(n=3\), or \(V(x)>0\) for \(n>3\), and \(p\) is a subcritical or critical exponent. To prove it, she uses Satah-Struwe technique and proves weighted nonlinear estimates in Besov spaces.

MSC:

35L70 Second-order nonlinear hyperbolic equations
35L15 Initial value problems for second-order hyperbolic equations
35B45 A priori estimates in context of PDEs
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