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Quadratic forms for the Liouville equation wtt + λ2a(t)w = 0 with applications to Kirchhoff equation
We introduce a set of quadratic forms for the solutions of the Liouville equation w_{tt}+ λ^2a(t)w = 0 . From these forms we derive estimates for the wave equation u_{tt} − a(t)Δu = 0 and then prove the global solvability for the Kirchhoff equation in suitable classes of not necessarily …