On the asymptotic boundedness of the energy of solutions of the wave equation \(u_{tt}-a(t)\Delta u=0\)

DOI10.1007/S11565-012-0148-6zbMath1326.35039OpenAlexW2015095754MaRDI QIDQ473504

Chiara Boiti, Renato Manfrin

Publication date: 24 November 2014

Published in: Annali dell'Università di Ferrara. Sezione VII. Scienze Matematiche (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11565-012-0148-6

zbMATH Keywords

energy estimatestime dependent propagation speed

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Stability in context of PDEs (35B35) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) A priori estimates in context of PDEs (35B45) Initial value problems for second-order hyperbolic equations (35L15)

Related Items (3)

A class of dissipative wave equations with time-dependent speed and damping ⋮ On the asymptotic behavior of the energy for evolution models with oscillating time-dependent damping ⋮ Stability for a nonlinear hyperbolic equation with time-dependent coefficients and boundary damping

Cites Work

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• \(L^p\)-\(L^q\) estimate for wave equation with bounded time dependent coefficient
• Quadratic forms for the Liouville equation \(w_{tt} + \lambda ^{2}a(t)w = 0\) with applications to Kirchhoff equation
• On the boundedness of solutions of the equation \(u^{\prime\prime}+(1+f(t))u=0\)
• Generalised energy conservation law for wave equations with variable propagation speed
• Lectures on nonlinear hyperbolic differential equations
• On the asymptotic behavior of the energy for the wave equations with time depending coefficients
• Lp Solutions of Second Order Differential Equations

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