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Decay rate estimates for a class of quasilinear hyperbolic equations with damping terms involving \(p\)-Laplacian. (English) Zbl 1304.35679

Summary: In this paper, we are concerned with the asymptotic behaviour of weak solutions to the initial boundary value problem for a class of quasilinear hyperbolic equations with damping terms involving \(p\)-Laplacian. By using the multiplier methods, we investigate the stability of weak solutions to the initial boundary value problem and obtain explicit decay rate estimation depending on strain-caused stress term and damping terms.{
©2014 American Institute of Physics}

MSC:

35Q74 PDEs in connection with mechanics of deformable solids
35L20 Initial-boundary value problems for second-order hyperbolic equations
35L72 Second-order quasilinear hyperbolic equations
35D30 Weak solutions to PDEs
35B40 Asymptotic behavior of solutions to PDEs
74D10 Nonlinear constitutive equations for materials with memory
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