Bifurcation of singular solutions in reversible systems and applications to reaction-diffusion equations

DOI10.1016/S0196-8858(82)80012-2zbMath0516.35010OpenAlexW2077302129MaRDI QIDQ1052522

Michael Renardy

Publication date: 1982

Published in: Advances in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0196-8858(82)80012-2

zbMATH Keywords

reversible systemsHopf bifurcationreaction-diffusion equationsbifurcation of singular solutionstrajectories connecting saddle points

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Bifurcations in context of PDEs (35B32)

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Stability of concatenated traveling waves ⋮ Derivation of amplitude equations and analysis of sideband instabilities in two-layer flows ⋮ Using Melnikov's method to solve Silnikov's problems ⋮ Time-periodic Ginzburg-Landau equations for one dimensional patterns with large wave length ⋮ Transition solutions in the Taylor problem ⋮ Essential instability of pulses and bifurcations to modulated travelling waves ⋮ Bifurcations in two-dimensional reversible maps ⋮ Stability of concatenated traveling waves: alternate approaches ⋮ Bifurcating time-periodic solutions of Navier-Stokes equations in infinite cylinders

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