Asymptotic behavior of solutions to the damped quasilinear equation \(\partial^ 2/\partial t^ 2 u(x,t) + \gamma \partial u/\partial t (x,t) - \partial/\partial x \sigma(\partial u/\partial t)\)

DOI10.1016/0022-247X(82)90143-3zbMath0506.35068OpenAlexW2080643686MaRDI QIDQ1836802

Frederick Bloom

Publication date: 1982

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-247x(82)90143-3

zbMATH Keywords

growth estimatesinitial-boundary conditionsdamped quasilinear equation

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Second-order nonlinear hyperbolic equations (35L70)

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Cites Work

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• Global existence, uniqueness, and asymptotic stability of classical smooth solutions in one-dimensional nonlinear thermoelasticity
• Instability of steady shearing flows in a non-linear viscoelastic fluid
• Energy methods for nonlinear hyperbolic volterra integrodifferential equations
• Remarks on the Asymptotic Behavior of Solutions to Damped Evolution Equations in Hilbert Space
• Instability and Nonexistence of Global Solutions to Nonlinear Wave Equations of the Form Pu tt = -Au + ℱ(u)

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