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Portugaliae Mathematica


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Volume 65, Issue 4, 2008, pp. 447–484
DOI: 10.4171/PM/1821

Published online: 2008-12-31

Quadratic forms for the Liouville equation wtt + λ2a(t)w = 0 with applications to Kirchhoff equation

Renato Manfrin[1]

(1) Università IUAV di Venezia, Italy

We introduce a set of quadratic forms for the solutions of the Liouville equation wtt + λ2a(t)w = 0. From these forms we derive estimates for the wave equation utta(tu = 0 and then prove the global solvability for the Kirchhoff equation in suitable classes of not necessarily smooth or small initial data.

Keywords: Liouville equation, Kirchhoff equation, global solvability

Manfrin Renato: Quadratic forms for the Liouville equation wtt + λ2a(t)w = 0 with applications to Kirchhoff equation. Port. Math. 65 (2008), 447-484. doi: 10.4171/PM/1821