Generic hyperbolicity for the equilibria of the one-dimensional parabolic equation\newline \(u_t=(a(x)u_x)+f(u)\)
type: Item
instance of: scholarly article
title: Generic hyperbolicity for the equilibria of the one-dimensional parabolic equation\newline \(u_t=(a(x)u_x)+f(u)\)
zbMATH Open document ID: 1063.35088
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2004-09-22T00:00:00Z
review text: This work is a continuation of the one published by the same author in [Proc. R. Soc. Edinb., Sect. A 123, No. 6, 1031--1040 (1993; Zbl 0832.35051)]. There, he stablished generic hyperbolicity for the same type of problem with respect to \(a\) and \(f\) if additional hypotheses were imposed on the equation. Here, he eliminates those additional requirements on the equilibria but at the price of imposing new ones on \(a\).
reviewed by: Domingo Salazar
Mathematics Subject Classification ID: 35K60
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35B05
zbMATH DE Number: 2101849
zbMATH Keywords: hyperbolic equilibrium
zbMATH Keywords: generic property
zbMATH Keywords: reaction-diffusion equation
author: Antônio L. Pereira
MaRDI profile type: Publication
full work available at URL: j.na.2003.10.003
OpenAlex ID: W2080361614
cites work: The Morse-Smale property for a semilinear parabolic equation
cites work: Generic properties of stationary state solutions of reaction-diffusion equations
cites work: The Morse-Smale structure of a generic reaction-diffusion equation in higher space dimension
cites work: Some infinite-dimensional Morse-Smale systems defined by parabolic partial differential equations
cites work: Generic hyperbolicity for scalar parabolic equations
cites work: Generic properties of equilibria of reaction-diffusion equations with variable diffusion
DOI: 10.1016/J.NA.2003.10.003
description: scientific article; zbMATH DE number 2101849