Numerical verification for existence of a global-in-time solution to semilinear parabolic equations

DOI10.1016/j.cam.2016.10.024zbMath1357.65051OpenAlexW2547056482MaRDI QIDQ729841

Akitoshi Takayasu, Makoto Mizuguchi, Takayuki Kubo, Shin'ichi Oishi

Publication date: 22 December 2016

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

Full work available at URL: https://doi.org/10.1016/j.cam.2016.10.024

zbMATH Keywords

semilinear parabolic equationsglobal-in-time solutionverified numerical computations

Mathematics Subject Classification ID

Initial-boundary value problems for second-order parabolic equations (35K20) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Algorithms with automatic result verification (65G20) Semilinear parabolic equations with Laplacian, bi-Laplacian or poly-Laplacian (35K91)

Related Items

Rigorous numerics for nonlinear heat equations in the complex plane of time, Numerical validation of blow-up solutions of ordinary differential equations, A rigorous implicit \(C^1\) Chebyshev integrator for delay equations, Global existence and blow-up of solutions for parabolic equations involving the Laplacian under nonlinear boundary conditions, A Method of Verified Computations for Solutions to Semilinear Parabolic Equations Using Semigroup Theory, Convergence analysis of the splitting method to the nonlinear heat equation, Numerical Verification of Solutions for Nonlinear Parabolic Problems, Pointwise a Posteriori Error Bounds for Blow-Up in the Semilinear Heat Equation, Rigorous numerical computations for 1D advection equations with variable coefficients, Rigorous FEM for One-Dimensional Burgers Equation

Uses Software

• INTLAB

Cites Work

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• On a posteriori estimates of inverse operators for linear parabolic initial-boundary value problems
• The value of the critical exponent for reaction-diffusion equations in cones
• On the critical exponent for reaction-diffusion equations
• Existence and multiplicity proofs for semilinear elliptic boundary value problems by computer assistance
• Semigroups of linear operators and applications to partial differential equations
• Blow-up of solutions of semilinear parabolic differential equations
• Asymptotic stability and blowing up of solutions of some nonlinear equations
• Decay of heat semigroups in \(L^\infty\) and applications to nonlinear parabolic problems in unbounded domains
• On the a posteriori estimates for inverse operators of linear parabolic equations with applications to the numerical enclosure of solutions for nonlinear problems
• Constructive A Priori Error Estimates for a Full Discrete Approximation of the Heat Equation
• On the Existence and Nonexistence of Global Solutions of Reaction-Diffusion Equations in Sectorial Domains
• A numerical approach to the proof of existence of solutions for elliptic problems
• Abstract Parabolic Evolution Equations and their Applications
• Geometry of unbounded domains,poincaré inequalities and stability in semilinear parabolic equations
• A Method of Verified Computations for Solutions to Semilinear Parabolic Equations Using Semigroup Theory
• Equivalent Norms for Sobolev Spaces