Validated integration of semilinear parabolic PDEs

Cites Work

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Efficient and generic algorithm for rigorous integration forward in time of dPDEs. I
Existence and stability of traveling pulse solutions of the FitzHugh-Nagumo equation
Existence of globally attracting fixed points of viscous Burgers equation with constant forcing. A computer assisted proof
Rigorous numerics for dissipative PDEs. III: An effective algorithm for rigorous integration of dissipative PDEs
Computer-assisted methods for the study of stationary solutions in dissipative systems, applied to the Kuramoto-Sivashinski equation
A geometric method for infinite-dimensional chaos: symbolic dynamics for the Kuramoto-Sivashinsky PDE on the line
Solving nonlinear parabolic problems with result verification. I: One- space dimensional case
Explicit \(H_ 2\)-estimates and pointwise bounds for solutions of second- order elliptic boundary value problems
Fourier-Taylor parameterization of unstable manifolds for parabolic partial differential equations: formalism, implementation and rigorous validation
Polynomial interpolation and a priori bootstrap for computer-assisted proofs in nonlinear ODEs
Rigorous numerics for ill-posed PDEs: periodic orbits in the Boussinesq equation
\(C^1\) Lohner algorithm.
Rigorous numerics for dissipative partial differential equations. II: Periodic orbit for the Kuramoto-Sivashinsky PDE -- a computer-assisted proof
Numerical verification of existence and inclusion of solutions for nonlinear operator equations
Rigorous numerics for ODEs using Chebyshev series and domain decomposition
Constructive error analysis of a full-discrete finite element method for the heat equation
Spontaneous periodic orbits in the Navier-Stokes flow
CAPD::DynSys: a flexible C++ toolbox for rigorous numerical analysis of dynamical systems
Rigorous numerics for nonlinear heat equations in the complex plane of time
A Taylor model toolbox for solving ODEs implemented in Matlab/INTLAB
Validated computations for connecting orbits in polynomial vector fields
Computer-assisted proofs in PDE: a survey
Fast construction of the Fejér and Clenshaw-Curtis quadrature rules
A computer-assisted existence and multiplicity proof for travelling waves in a nonlinearly supported beam
Auswertung der Normen von Interpolationsoperatoren
Rigorous numerics in dynamics
Integration of Dissipative Partial Differential Equations: A Case Study
A numerical approach to the proof of existence of solutions for elliptic problems
Validated Continuation for Equilibria of PDEs
A Numerical Verification Method for Solutions of Boundary Value Problems with Local Uniqueness by Banach's Fixed-Point Theorem
Introduction to rigorous numerics in dynamics: General functional analytic setup and an example that forces chaos
Computer-Assisted Proof of Heteroclinic Connections in the One-Dimensional Ohta--Kawasaki Model
Rigorously Computing Symmetric Stationary States of the Ohta--Kawasaki Problem in Three Dimensions
Attracting Fixed Points for the Kuramoto--Sivashinsky Equation: A Computer Assisted Proof
Numerical Verification of Solutions for Nonlinear Parabolic Problems
Existence of Globally Attracting Solutions for One-Dimensional Viscous Burgers Equation with Nonautonomous Forcing---A Computer Assisted Proof
Numerical Computations and Computer Assisted Proofs of Periodic Orbits of the Kuramoto--Sivashinsky Equation
Numerical Verification Methods and Computer-Assisted Proofs for Partial Differential Equations
A Posteriori Verification of Invariant Objects of Evolution Equations: Periodic Orbits in the Kuramoto--Sivashinsky PDE
Rigorous numerics for partial differential equations: The Kuramoto-Sivashinsky equation
Validated numerical approximation of stable manifolds for parabolic partial differential equations
Validated forward integration scheme for parabolic PDEs via Chebyshev series