Computation of smooth manifolds via rigorous multi-parameter continuation in infinite dimensions

DOI10.1007/s10208-015-9259-7zbMath1347.65102OpenAlexW289966560MaRDI QIDQ285445

Jean-Philippe Lessard, Alessandro Pugliese, Marcio Gameiro

Publication date: 19 May 2016

Published in: Foundations of Computational Mathematics (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/20.500.11794/1468

zbMATH Keywords

Cahn-Hilliard equationcontinuation methodBanach spacenonlinear equationscontraction mappingcontraction methodssimplicial approximationssimplicial triangulationstwo-dimmensional manifolds

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09) A priori estimates in context of PDEs (35B45) Numerical solutions to equations with nonlinear operators (65J15) Bifurcations in context of PDEs (35B32)

Related Items (17)

Microscopic patterns in the 2D phase-field-crystal model ⋮ Connecting Orbits for Compact Infinite Dimensional Maps: Computer Assisted Proofs of Existence ⋮ Rigorous enclosures of solutions of Neumann boundary value problems ⋮ Continuation of solutions and studying delay differential equations via rigorous numerics ⋮ Existence of traveling wave solutions for the Diffusion Poisson Coupled Model: a computer-assisted proof ⋮ Computer-Assisted Proof of Heteroclinic Connections in the One-Dimensional Ohta--Kawasaki Model ⋮ Computational techniques to locate crossing/sliding regions and their sets of attraction in non-smooth dynamical systems ⋮ Validation of the bifurcation diagram in the 2D Ohta–Kawasaki problem ⋮ Periodic orbits in Hořava-Lifshitz cosmologies ⋮ A Posteriori Validation of Generalized Polynomial Chaos Expansions ⋮ Validated Computation of Heteroclinic Sets ⋮ Automatic differentiation for Fourier series and the radii polynomial approach ⋮ A general framework for validated continuation of periodic orbits in systems of polynomial ODEs ⋮ Rigorous numerics for analytic solutions of differential equations: the radii polynomial approach ⋮ Critical homoclinics in a restricted four-body problem: numerical continuation and center manifold computations ⋮ Rigorous Verification of Hopf Bifurcations via Desingularization and Continuation ⋮ Rigorous validation of stochastic transition paths

Uses Software

• INTLAB
• galepu

Cites Work

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