The dynamics of a one-dimensional parabolic problem versus the dynamics of its discretization

DOI10.1006/jdeq.2000.3878zbMath0966.35056OpenAlexW2067306155MaRDI QIDQ1592709

Simone M. Bruschi, José Gaspar Ruas-Filho, Alexandre Nolasco De Carvalho

Publication date: 7 August 2001

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

Full work available at URL: http://hdl.handle.net/11449/25114

zbMATH Keywords

Neumann boundary conditionspatial semidiscretizationtopological equivalence of attractors

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Attractors (35B41) Initial-boundary value problems for second-order parabolic equations (35K20) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06)

Related Items (4)

CONTROLLING CHAOS TO A CLASS OF PDEs BY APPLYING INVARIANT MANIFOLD AND STRUCTURE STABILITY THEORY ⋮ Continuity of the attractors in a singular problem arising in composite materials ⋮ SYNCHRONIZATION OF SOME KIND OF PDE CHAOTIC SYSTEMS BY INVARIANT MANIFOLD METHOD ⋮ A General Approximation Scheme for Attractors of Abstract Parabolic Problems

Cites Work

• Some infinite-dimensional Morse-Smale systems defined by parabolic partial differential equations
• Geometric theory of semilinear parabolic equations
• Asymptotic behavior for solutions of a one-dimensional parabolic equation with homogeneous Neumann boundary conditions
• Instability results for reaction-diffusion equations with Neumann boundary conditions
• Upper semicontinuity of attractors and synchronization
• A scalar parabolic equation whose asymptotic behavior is dictated by a system of ordinary differential equations
• Jacobi matrices and transversality
• A bifurcation problem for a nonlinear partial differential equation of parabolic type^†
• Orbit equivalence of global attractors of semilinear parabolic differential equations
• Attractors of parabolic problems with nonlinear boundary conditions. uniform bounds
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