On the mathematical foundations of elastic stability theory. I

DOI10.1007/BF00253224zbMath0488.73043MaRDI QIDQ1166316

Michel Potier-Ferry

Publication date: 1982

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

zbMATH Keywords

conservative loadsdynamic response is viscoelasticenergy criterion is sufficient condition for Lyapunov stabilityLyapunov stability of equilibrium statesthree- dimensional Kelvin-Voigt viscoelastic modelthree-dimensional hyperelastic bodiesW-2,P norm

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Nonlinear elasticity (74B20) Stability of dynamical problems in solid mechanics (74H55) Dynamical problems in solid mechanics (74H99) Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials) (74D99) Equilibrium (steady-state) problems in solid mechanics (74G99)

Related Items

Smoothing effect and large time behavior of solutions to nonlinear elastic wave equations with viscoelastic term ⋮ Quasistatic nonlinear viscoelasticity and gradient flows ⋮ On the positivity of the second variation in finite elasticity ⋮ Dynamical modelling of phase transitions by means of viscoelasticity in many dimensions ⋮ The linearization principle for the stability of solutions of quasilinear parabolic equations. I ⋮ Global existence and exponential stability of small solutions to nonlinear viscoelasticity ⋮ Stability for second order abstract evolution equations ⋮ An existence result for a class of second order evolution equations of mixed type ⋮ Inversion analysis for magnetic resonance elastography ⋮ Quasiconvexity at the boundary, positivity of the second variation and elastic stability ⋮ Asymptotic behavior of an elastic satellite with internal friction

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• The linearization principle for the stability of solutions of quasilinear parabolic equations. I
• Well-posed quasi-linear second-order hyperbolic systems with applications to nonlinear elastodynamics and general relativity
• Convexity conditions and existence theorems in nonlinear elasticity
• The elastic instability of a director rod
• Dynamic stability of one-dimensional nonlinearly viscoelastic bodies
• Existence and nonexistence in the large of solutions of quasilinear wave equations
• Espaces d'interpolation et théorème de Soboleff
• Caractérisation de quelques espaces d'interpolation
• The mixed initial-boundary value problem for the equations of nonlinear one-dimensional viscoelasticity
• On the eigenfunctions and on the eigenvalues of general elliptic boundary value problems
• Formation of singularities in one-dimensional nonlinear wave propagation
• A model for one-dimensional, nonlinear viscoelasticity
• Development of Singularities of Solutions of Nonlinear Hyperbolic Partial Differential Equations
• Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II