Some uniqueness and continuous dependence theorems for nonlinear elastodynamics in exterior domains

DOI10.1080/00036818308839438zbMath0478.73006OpenAlexW1967999549WikidataQ58295824 ScholiaQ58295824MaRDI QIDQ3936268

Lawrence E. Payne, Robin J. Knops

Publication date: 1983

Published in: Applicable Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00036818308839438

zbMATH Keywords

velocitynonlinear elastodynamicsexterior domainsinitial boundary value problemstress componentsnonlinear hyperelastic bodiesHölder continuous dependenceintroduces weighted integrals into logarithmic convexity and concavity argumentsmild asymptotic behaviour on displacementnull solution is unique

Mathematics Subject Classification ID

Nonlinear elasticity (74B20) Uniqueness of solutions of dynamical problems in solid mechanics (74H25) Uniqueness of solutions of equilibrium problems in solid mechanics (74G30)

Related Items (3)

Uniqueness and continuous dependence in the linear elastodynamic exterior and half-space problems ⋮ The Lagrange identity method in linear thermoelasticity ⋮ Continuous dependence and uniqueness theorems in boundary‐initial value problems for a class of porous bodies occupying bounded or unbounded domains

Cites Work

• Unnamed Item
• Sul teorema di unicita nella dinamica dei fluidi
• Non-existence, instability, and growth theorems for solutions of a class of abstract nonlinear equations with applications to nonlinear elasto- dynamics
• Growth estimates and lower bounds for solutions in nonlinear elastodynamics with indefinite strain energy
• A uniqueness theorem for hydrodynamic flows in unbounded domains
• Uniqueness and continuous dependence theorem for the conduction-diffusion solution to the Boussinesq equations on an exterior domain
• Continuous dependence theorems in linear elasticity on exterior domains
• Uniqueness theorems for displacement fields with locally finite energy in linear elastostatics
• Stability in linear elasticity
• Logarithmic convexity and the Cauchy problem for some abstract second order differential inequalities
• On uniqueness and continuous dependence in dynamical problems of linear thermoelasticity
• Qualitative Results for a Class of General Materials
• Continuous data dependence in linear elastodynamics on unbounded domains without definiteness conditions on the elasticities
• Lower Bounds and Uniqueness Theorems for Solutions of Differential Equations in a Hilbert Space
• The domain of dependence inequality for symmetric hyperbolic systems

This page was built for publication: Some uniqueness and continuous dependence theorems for nonlinear elastodynamics in exterior domains