Quadratic forms for the Liouville equation \(w_{tt} + \lambda ^{2}a(t)w = 0\) with applications to Kirchhoff equation (Q959457)
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scientific article; zbMATH DE number 5381761
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Quadratic forms for the Liouville equation \(w_{tt} + \lambda ^{2}a(t)w = 0\) with applications to Kirchhoff equation |
scientific article; zbMATH DE number 5381761 |
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Quadratic forms for the Liouville equation \(w_{tt} + \lambda ^{2}a(t)w = 0\) with applications to Kirchhoff equation (English)
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11 December 2008
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Summary: We introduce a set of quadratic forms for the solutions of the Liouville equation \(w_{tt} + \lambda ^{2}a(t)w = 0\). From these forms we derive estimates for the wave equation \(u_{tt} - a(t)\Delta u = 0\) and then prove the global solvability for the Kirchhoff equation in suitable classes of not necessarily smooth or small initial data.
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Liouville equation
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Kirchhoff equation
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global solvability
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nonsmooth large data
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