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Dynamics of threshold solutions for energy-critical wave equation. (English) Zbl 1159.35043

The initial value problem to the equation \(u_{tt}-\Delta u-\left| u\right| ^{\frac{4}{n-2}}u=0\) for the dimensions \(n=3,4,5 \) is treated. The authors give a classification of the solutions, not necessarily radial, with critical energy corresponding the energy of the stationary solution. The existence of two special radial solutions connecting different behavior for negative and positive times is proved.

MSC:

35L70 Second-order nonlinear hyperbolic equations
35B40 Asymptotic behavior of solutions to PDEs
35L15 Initial value problems for second-order hyperbolic equations
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