22 citations · 50 across the 17 of their papers we have counts for
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A Framework for the Numerical Computation and a Posteriori Verification of Invariant Objects of Evolution Equations
Jordi-Lluís Figueras, Marcio Gameiro, Jean Philippe Lessard +1
We develop a theoretical framework for computer-assisted proofs of the existence of invariant objects in semilinear PDEs. The invariant objects considered in this paper are equilib…
Numerical Computations and Computer Assisted Proofs of Periodic Orbits of the Kuramoto-Sivashinsky Equation
Jordi-Lluís Figueras, Rafael de la Llave
We present numerical results and computer assisted proofs of the existence of periodic orbits for the Kuramoto-Sivashinky equation. These two results are based on writing down the…
An a posteriori KAM theorem for whiskered tori in Hamiltonian partial differential equations with applications to some ill-posed equations
Rafael de la Llave, Yannick Sire
The goal of this paper is to develop a KAM theory for tori with hyperbolic directions, which applies to Hamiltonian partial differential equations, even to some ill-posed ones. The…