A computer-assisted proof of the existence of solutions to a boundary value problem with an integral boundary condition

DOI10.1016/J.CNSNS.2010.07.008zbMath1221.35233OpenAlexW2083229704MaRDI QIDQ718434

Gunilla Kreiss, Oswald Fogelklou, Warwick Tucker, Malin Siklosi

Publication date: 23 September 2011

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cnsns.2010.07.008

zbMATH Keywords

existencenumerical verificationtwo-point boundary value problemscomputer-assisted proofenclosureviscous Burgers equationfixed-point problems

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Hyperbolic conservation laws (35L65) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Software, source code, etc. for problems pertaining to partial differential equations (35-04) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (3)

A posteriori error bounds for two point boundary value problems: a Green's function approach ⋮ Rigorous numerics for ODEs using Chebyshev series and domain decomposition ⋮ Computer-assisted proofs in PDE: a survey

Uses Software

• INTLAB
• RODES

Cites Work

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• Exact solutions of equations for the Burgers hierarchy
• Self-similar solutions of the Burgers hierarchy
• A numerical verification method for the existence of weak solutions for nonlinear boundary value problems
• Verified integration of ODEs and flows using differential algebraic methods on high-order Taylor models
• A rigorous ODE solver and Smale's 14th problem
• A Numerical Verification Method for Solutions of Boundary Value Problems with Local Uniqueness by Banach's Fixed-Point Theorem
• Attracting Fixed Points for the Kuramoto--Sivashinsky Equation: A Computer Assisted Proof
• Solutions in the large for nonlinear hyperbolic systems of equations
• The partial differential equation u_t + uu_x = μ_xx
• On a quasi-linear parabolic equation occurring in aerodynamics
• Front tracking for hyperbolic conservation laws
• Computer-assisted enclosure methods for elliptic differential equations
• Rigorous numerics for partial differential equations: The Kuramoto-Sivashinsky equation

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