Rigorous numerics for nonlinear heat equations in the complex plane of time

DOI10.1007/s00211-022-01291-2OpenAlexW2982262031MaRDI QIDQ2149062

Jonathan Jaquette, Jean-Philippe Lessard, Akitoshi Takayasu, Hisashi Okamoto

Publication date: 28 June 2022

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1910.12472

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear parabolic equations (35K55) Analyticity in context of PDEs (35A20) General methods in interval analysis (65G40) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Blow-up in context of PDEs (35B44) Numerical analysis (65-XX)

Related Items (2)

Validated numerical approximation of stable manifolds for parabolic partial differential equations ⋮ Blow up in a periodic semilinear heat equation

Uses Software

• INTLAB
• Chebfun
• GitHub

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A blow-up problem for a nonlinear heat equation in the complex plane of time
• Numerical validation of blow-up solutions of ordinary differential equations
• Efficient and generic algorithm for rigorous integration forward in time of dPDEs. I
• Analytic solutions of some nonlinear diffusion equations
• Numerical verification for existence of a global-in-time solution to semilinear parabolic equations
• Numerical validation of blow-up solutions with quasi-homogeneous compactifications
• A geometric method for infinite-dimensional chaos: symbolic dynamics for the Kuramoto-Sivashinsky PDE on the line
• Covering relations, cone conditions and the stable manifold theorem
• Semigroups of linear operators and applications to partial differential equations
• Computing discrete convolutions with verified accuracy via Banach algebras and the FFT.
• Singularities and heteroclinic connections in complex-valued evolutionary equations with a quadratic nonlinearity
• Global dynamics in nonconservative nonlinear Schrödinger equations
• Rigorous numerical verification of uniqueness and smoothness in a surface growth model
• Blow-up profile for solutions of a fourth order nonlinear equation
• On the a posteriori estimates for inverse operators of linear parabolic equations with applications to the numerical enclosure of solutions for nonlinear problems
• Chebfun: A New Kind of Numerical Computing
• Stationary Coexistence of Hexagons and Rolls via Rigorous Computations
• A Method of Verified Computations for Solutions to Semilinear Parabolic Equations Using Semigroup Theory
• Rigorous Numerics for Nonlinear Differential Equations Using Chebyshev Series
• Dynamics of evolutionary equations

This page was built for publication: Rigorous numerics for nonlinear heat equations in the complex plane of time