Multidimensional viscoelasticity equations with nonlinear damping and source terms.

DOI10.1016/J.NA.2003.07.021zbMath1057.74007OpenAlexW1997655087MaRDI QIDQ1426714

Junsheng Zhao, Ya-Cheng Liu

Publication date: 15 March 2004

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2003.07.021

zbMATH Keywords

existenceglobal solutionspotential wellvacuum isolation

Mathematics Subject Classification ID

Initial-boundary value problems for second-order hyperbolic equations (35L20) Nonlinear constitutive equations for materials with memory (74D10) Existence of solutions of dynamical problems in solid mechanics (74H20)

Related Items (14)

Fourth order wave equations with nonlinear strain and source terms ⋮ Exponential decay of energy for some nonlinear hyperbolic equations with strong dissipation ⋮ Existence and blow up for a nonlinear hyperbolic equation with anisotropy ⋮ Global existence, nonexistence, and decay of solutions for a viscoelastic wave equation with nonlinear boundary damping and source terms ⋮ A class of fourth order wave equations with dissipative and nonlinear strain terms ⋮ Global well-posedness for a class of fourth-order nonlinear strongly damped wave equations ⋮ Global existence, blow up and asymptotic behaviour of solutions for nonlinear Klein-Gordon equation with dissipative term ⋮ Potential well method for Cauchy problem of generalized double dispersion equations ⋮ Blow-up of solutions for a viscoelastic equation with nonlinear damping ⋮ Global nonexistence of solutions for systems of quasilinear hyperbolic equations with damping and source terms ⋮ On potential wells and applications to semilinear hyperbolic equations and parabolic equations ⋮ Global existence and asymptotic behavior of solutions for some nonlinear hyperbolic equation ⋮ Viscous solutions on some nonlinear wave equations ⋮ Non-global solution for visco-elastic dynamical system with nonlinear source term in control problem

Cites Work

• Some remarks on the equation \(y_{tt}-\sigma (y_x)y_{xx}-y_{x^tx}=f\)
• Asymptotic behaviour and changes of phase in one-dimensional nonlinear viscoelasticity
• A quasilinear hyperbolic and related third-order equations
• On potential wells and vacuum isolating of solutions for semilinear wave equations
• On the existence, uniqueness, and stability of solutions of the equation \(p_0 {\mathfrak X}_{tt} = E({\mathfrak X}_ x) {\mathfrak X}_{xx} +\lambda {\mathfrak X}_{xxt}\)
• The mixed initial-boundary value problem for the equations of nonlinear one-dimensional viscoelasticity
• On the exponential stability of solutions of \(E(u_ x)u_{xx} + \lambda u_{xtx} = \rho u_{tt}\)
• Blowup of solutions for a class of quasilinear evolution equations
• Strong Solutions of a Quasilinear Wave Equation with Nonlinear Damping
• On the Existence and Uniqueness of Solutions of the Equation
• Existence and asymptotic behaviour of solutions for a class of quasi-linear evolution equations with non-linear damping and source terms
• Existence Theorems for a Quasilinear Evolution Equation
• On the existence of solutions to the equation \(u_{tt}=u_{xxt}+\sigma (u_x)_x\)
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