\(L^{p}-L^{q}\) estimates for wave equations and the Kirchhoff equation (Q935580)
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scientific article; zbMATH DE number 5309639
| Language | Label | Description | Also known as |
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| English | \(L^{p}-L^{q}\) estimates for wave equations and the Kirchhoff equation |
scientific article; zbMATH DE number 5309639 |
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\(L^{p}-L^{q}\) estimates for wave equations and the Kirchhoff equation (English)
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11 August 2008
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The paper refers to the Cauchy problem for the wave equation with time-dependent coefficients. In case coefficients are of Lipschitz class, are assumed to satisfy some additional conditions and norms of data are finite, a decay estimate for solution is obtained. As technique one applies Fourier transform to the wave equation and initial data and one develops the asymptotic integration of the ODE. As an application, using the fixed point theorem of Schauder, estimates for the solution of Kirchhoff equation are determined.
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wave equation
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decay estimate
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Fourier transform
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Kirchhiff equation
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fixed point theorem of Schauder
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