A topological degree for orbits connecting critical points of autonomous systems

DOI10.1016/0022-0396(80)90003-0zbMath0417.34053OpenAlexW2074884623MaRDI QIDQ755021

M. S. Mock

Publication date: 1980

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-0396(80)90003-0

zbMATH Keywords

critical pointstopological degreeshock wavesnonlinear conservation lawsMorse indicesautonomous system

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Nonlinear ordinary differential equations and systems (34A34) Shock waves and blast waves in fluid mechanics (76L05) Fixed-point and coincidence theorems (topological aspects) (54H25) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) General theory for ordinary differential equations (34A99)

Related Items (13)

Géométrie des systèmes hyperboliques de lois de conservation ⋮ A class of hyperbolic systems of conservation laws satisfying weaker conditions than genuine nonlinearity ⋮ Strong viscous shocks for systems of conservation laws with a high order of dissipation ⋮ Existence and stability of travelling wave solutions of competition models. A degree theoretic approach ⋮ Dispersion and shock-wave structure ⋮ Linear stability of shock profiles for systems of conservation laws with semi-linear relaxation ⋮ On travelling-wave solutions to systems of conservation laws with singular viscosity ⋮ Existence in the Large for Riemann Problems for Systems of Conservation Laws ⋮ Nonexistence of Riemann solutions and Majda-Pego instability ⋮ The Riemann problem for fluid flow of real materials ⋮ VISCOUS SHOCK PROFILES FOR 2 × 2 SYSTEMS OF HYPERBOLIC CONSERVATION LAWS WITH AN UMBILIC POINT ⋮ Stable viscosity matrices for systems of conservation laws ⋮ On the oscillatory solutions in hyperbolic conservation laws

Cites Work

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• Shock waves as limits of progressive wave solutions of higher order equations, II
• Systems of Conservation Equations with a Convex Extension
• Shock waves as limits of progressive wave solutions of higher order equations
• The profile of a steady plane shock wave

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