Generic hyperbolicity for the equilibria of the one-dimensional parabolic equation\newline \(u_t=(a(x)u_x)+f(u)\)

DOI10.1016/J.NA.2003.10.003zbMath1063.35088OpenAlexW2080361614MaRDI QIDQ1879174

Antonio Luiz Pereira

Publication date: 22 September 2004

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2003.10.003

zbMATH Keywords

generic propertyreaction-diffusion equationhyperbolic equilibrium

Mathematics Subject Classification ID

Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations (35K60) Reaction-diffusion equations (35K57) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05)

Related Items (3)

Generic simplicity of the eigenvalues for a supported plate equation ⋮ Adaptation of the generic PDE's results to the notion of prevalence ⋮ Generic hyperbolicity of stationary solutions for a reaction-diffusion system

Cites Work

• The Morse-Smale structure of a generic reaction-diffusion equation in higher space dimension
• Generic properties of stationary state solutions of reaction-diffusion equations
• Some infinite-dimensional Morse-Smale systems defined by parabolic partial differential equations
• The Morse-Smale property for a semilinear parabolic equation
• Generic properties of equilibria of reaction-diffusion equations with variable diffusion
• Generic hyperbolicity for scalar parabolic equations

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