Decay rate of quasilinear wave equation with viscosity

DOI10.1007/s10255-012-0172-4zbMath1255.35049OpenAlexW2072235524MaRDI QIDQ692692

Shu-xian Deng, Xin Liu, Yu-ming Qin

Publication date: 6 December 2012

Published in: Acta Mathematicae Applicatae Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10255-012-0172-4

zbMATH Keywords

energy inequalityenergy perturbation methodcomparison lemma

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Initial-boundary value problems for second-order hyperbolic equations (35L20) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Initial value problems for second-order hyperbolic equations (35L15) Higher-order quasilinear hyperbolic equations (35L77)

Cites Work

• Some remarks on the equation \(y_{tt}-\sigma (y_x)y_{xx}-y_{x^tx}=f\)
• Global existence and exponential stability of small solutions to nonlinear viscoelasticity
• On a global in time existence theorem of smooth solutions to a nonlinear wave equation with viscosity
• Energy decay for the quasilinear wave equation with viscosity
• On the existence, uniqueness, and stability of solutions of the equation \(p_0 {\mathfrak X}_{tt} = E({\mathfrak X}_ x) {\mathfrak X}_{xx} +\lambda {\mathfrak X}_{xxt}\)
• Decay rate of solutions of a wave equation with damping and external force
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