Stable patterns for fourth-order parabolic equations
type: Item
instance of: scholarly article
title: Stable patterns for fourth-order parabolic equations
zbMATH Open document ID: 1020.35027
DOI: 10.1215/S0012-7094-02-11534-8
published in: Duke Mathematical Journal
publication date: 2003-10-06T00:00:00Z
review text: The authors study the following model equations \[ u_t=-\gamma u_{xxxx}+\beta u_{xx}- F'(u),\quad (t,x)\in\mathbb{R}^+\times (0,L), \] with \(\gamma> 0\), \(\beta> 0\). Their goal is to study stable stationary states as a function of the parameters \(\gamma\), \(\beta\), the potential \(F\), the intervallength \(L\), and the boundary conditions at \(x= 0\) and \(x\in L\). To this end they develop a new variational gluing method for constructing stable stationary states.
Mathematics Subject Classification ID: 35K35
Mathematics Subject Classification ID: 35K55
zbMATH DE Number: 1877092
zbMATH Keywords: variational gluing method
author: Jan Bouwe Van den Berg
author: Robert Vandervorst
reviewed by: Messoud Efendiev
describes a project that uses: AUTO
MaRDI profile type: Publication
cites work: The Morse-Smale property for a semilinear parabolic equation
cites work: Bifurcation theory for symmetric potential operators and the equivariant cup-length
cites work: Uniqueness of solutions for the extended Fisher-Kolmogorov equation
cites work: The phase-plane picture for a class of fourth-order conservative differential equations
cites work: Q4784604
cites work: Global branches of multi-bump periodic solutions of the Swift-Hohenberg equation
cites work: Second order Lagrangian twist systems: simple closed characteristics
cites work: Bifurcation and coalescence of a plethora of homoclinic orbits for a Hamiltonian system
cites work: A global condition for quasi-random behavior in a class of conservative systems
cites work: A bifurcation problem for a nonlinear partial differential equation of parabolic type†
cites work: On the thermodynamics of periodic phases
cites work: On the variational principle
cites work: Bifurcation for odd potential operators and an alternative topological index
cites work: Closed characteristics of fourth-order twist systems via braids
cites work: Morse theory on spaces of braids and Lagrangian dynamics
cites work: Q4039920
cites work: Geometric theory of semilinear parabolic equations
cites work: Some infinite-dimensional Morse-Smale systems defined by parabolic partial differential equations
cites work: Homotopy classes for stable periodic and chaotic patterns in fourth-order Hamiltonian systems
cites work: Homotopy classes for stable connections between Hamiltonian saddle-focus equilibria
cites work: Multitransition homoclinic and heteroclinic solutions of the extended Fisher-Kolmogorov equation
cites work: Slow motion in higher-order systems and \(\Gamma\)-convergence in one space dimension
cites work: Uniqueness of the stationary wave for the extended Fisher-Kolmogorov equation
cites work: Q3961188
cites work: Global Asymptotic Dynamics of Gradient-Like Bistable Equations
cites work: Periodic phases in second-order materials
cites work: Spatial patterns described by the extended Fisher-Kolmogorov (EFK) equation: Kinks
cites work: A topological shooting method and the existence of kinks of the extended Fisher-Kolmogorov equation
cites work: Chaotic spatial patterns described by the extended Fisher-Kolmogorov equation
cites work: Spatial Patterns Described by the Extended Fisher--Kolmogorov Equation: Periodic Solutions
cites work: Q4888372
cites work: Non-existence and uniqueness results for fourth-order Hamiltonian systems
cites work: Stability of multiple-pulse solutions
cites work: Heteroclinic tangles and homoclinic snaking in the unfolding of a degenerate reversible Hamiltonian-Hopf bifurcation
description: scientific article; zbMATH DE number 1877092