Rigorous computation of solutions of semilinear PDEs on unbounded domains via spectral methods
DOI10.1137/23M1607507zbMATH Open1547.35186MaRDI QIDQ6598405
Jean-Philippe Lessard, Jean-Christophe Nave, Matthieu Cadiot
Publication date: 5 September 2024
Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)
Fourier analysisunbounded domainscomputer-assisted proofNewton-Kantorovich theoremstability of traveling wavessemilinear PDEs
Periodic solutions to PDEs (35B10) Nonlinear higher-order PDEs (35G20) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Fourier coefficients, Fourier series of functions with special properties, special Fourier series (42A16) Series expansions (e.g., Taylor, Lidstone series, but not Fourier series) (41A58) Semilinear elliptic equations (35J61) Soliton solutions (35C08) Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals (35A23) Strong solutions to PDEs (35D35)
Cites Work
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- Rigorous numerics for nonlinear operators with tridiagonal dominant linear part
- Linear and semilinear partial differential equations. An introduction
- Verified bounds for singular values, in particular for the spectral norm of a matrix and its inverse
- A framework of verified eigenvalue bounds for self-adjoint differential operators
- Analytic estimates and rigorous continuation for equilibria of higher-dimensional PDEs
- A geometric method for infinite-dimensional chaos: symbolic dynamics for the Kuramoto-Sivashinsky PDE on the line
- New solitary wave solutions to the Kuramoto-Sivashinsky and the Kawahara equations
- Periodic and solitary wave solutions of Kawahara and modified Kawahara equations by using Sine-Cosine method
- Numerical methods in bifurcation problems. Lectures delivered at the Indian Institute of Science, Bangalore, under the T.I.F.R.-I.I.Sc. Programme in Applications of Mathematics. Notes by A. K. Nandakumaran and Mythily Ramaswamy
- New exact travelling wave solutions for the Kawahara and modified Kawahara equations
- A rigorous ODE solver and Smale's 14th problem
- A construction of two different solutions to an elliptic system
- Continuation of homoclinic orbits in the suspension bridge equation: a computer-assisted proof
- A proof of Wright's conjecture
- Perturbation theory for linear operators.
- A stability analysis of fifth-order water wave models
- Spatial periodic orbits in the equilateral circular restricted four-body problem: computer-assisted proofs of existence
- Spontaneous periodic orbits in the Navier-Stokes flow
- Equilibrium validation in models for pattern formation based on Sobolev embeddings
- A new formulation using the Schur complement for the numerical existence proof of solutions to elliptic problems: without direct estimation for an inverse of the linearized operator
- Verified norm estimation for the inverse of linear elliptic operators using eigenvalue evaluation
- Validated computations for connecting orbits in polynomial vector fields
- An improved method for verifying the existence and bounds of the inverse of second-order linear elliptic operators mapping to dual space
- Computer-assisted proofs in PDE: a survey
- A numerical method to verify the invertibility of linear elliptic operators with applications to nonlinear problems
- The parameterization method for invariant manifolds. III: Overview and applications
- Eigenvalue inclusions via domain decomposition
- NUMERICAL VERIFICATION METHODS FOR SOLUTIONS OF ORDINARY AND PARTIAL DIFFERENTIAL EQUATIONS
- Rigorous numerics in dynamics
- Shock Waves in Dispersive Hydrodynamics with Nonconvex Dispersion
- Fourier analysis and partial differential equations
- Julia: A Fresh Approach to Numerical Computing
- Computer Assisted Fourier Analysis in Sequence Spaces of Varying Regularity
- Fourier Analysis and Nonlinear Partial Differential Equations
- Rigorous Numerics for Symmetric Connecting Orbits: Even Homoclinics of the Gray–Scott Equation
- A numerical approach to the proof of existence of solutions for elliptic problems II
- Global smooth solution curves using rigorous branch following
- Existence and dynamic stability of solitary wave solutions of equations arising in long wave propagation
- A computer-assisted proof of the Feigenbaum conjectures
- Positivity Properties and Stability of Solitary–Wave Solutions of Model Equations For Long Waves
- The Lorenz attractor exists
- Chaos in the Lorenz equations: a computer-assisted proof
- The parameterization method for invariant manifolds I: Manifolds associated to non-resonant subspaces
- The parameterization method for invariant manifolds II: regularity with respect to parameters
- Rigorously Computing Symmetric Stationary States of the Ohta--Kawasaki Problem in Three Dimensions
- Torus knot choreographies in the n-body problem
- Computer-Assisted Proofs in Analysis and Programming in Logic: A case Study
- 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
- Constructive proofs for localised radial solutions of semilinear elliptic systems on Rd
- Smooth self-similar imploding profiles to 3D compressible Euler
- Validated forward integration scheme for parabolic PDEs via Chebyshev series
- Computer-assisted proofs for some nonlinear diffusion problems
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