Stability and Hopf Bifurcation for Fully Nonlinear Parabolic-Hyperbolic Equations

DOI10.1137/S003614109833793XzbMath1049.35145OpenAlexW1996741937MaRDI QIDQ4509957

Stuart S. Antman, Herbert Koch

Publication date: 19 October 2000

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/s003614109833793x

zbMATH Keywords

Hopf bifurcationnonlinear viscoelasticityoblique boundary conditionsfully nonlinear parabolic-hyperbolic equationslinearized satability

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) Stability of dynamical problems in solid mechanics (74H55) PDEs of mixed type (35M10) Linear constitutive equations for materials with memory (74D05) Stability problems for infinite-dimensional dissipative dynamical systems (37L15) Bifurcations in context of PDEs (35B32)

Related Items (7)

Dynamical problems for geometrically exact theories of nonlinearly viscoelastic rods ⋮ The motion of a particle on a light viscoelastic bar: asymptotic analysis of its quasilinear parabolic-hyperbolic equation. ⋮ Hopf bifurcation for a maturity structured population dynamic model ⋮ Error estimate of fully discrete discontinuous Galerkin approximation for the viscoelasticity type equation ⋮ The parabolic-hyperbolic system governing the spatial motion of nonlinearly viscoelastic rods ⋮ Hopf bifurcation in a size-structured population dynamic model with random growth ⋮ Rigorous verification of Hopf bifurcations in functional differential equations of mixed type

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