5 citations · 6 across the 6 of their papers we have counts for
6 papers
Validated integration of semilinear parabolic PDEs
Jan Bouwe van den Berg, Maxime Breden, Ray Sheombarsing
Integrating evolutionary partial differential equations (PDEs) is an essential ingredient for studying the dynamics of the solutions. Indeed, simulations are at the core of scienti…
Constructive proofs for localized radial solutions of semilinear elliptic systems on
Jan Bouwe van den Berg, Olivier Hénot, Jean-Philippe Lessard
Ground state solutions of elliptic problems have been analyzed extensively in the theory of partial differential equations, as they represent fundamental spatial patterns in many m…
Towards computational Morse-Floer homology: forcing results for connecting orbits by computing relative indices of critical points
Jan Bouwe van den Berg, Marcio Gameiro, Jean-Philippe Lessard +1
To make progress towards better computability of Morse-Floer homology, and thus enhance the applicability of Floer theory, it is essential to have tools to determine the relative i…
Validated Numerical Approximation of Stable Manifolds for Parabolic Partial Differential Equations
Jan Bouwe van den Berg, Jonathan Jaquette, J. D. Mireles James
This paper develops validated computational methods for studying infinite dimensional stable manifolds at equilibrium solutions of parabolic PDEs, synthesizing disparate errors res…
A proof of Wright's conjecture
Jan Bouwe van den Berg, Jonathan Jaquette
Wright's conjecture states that the origin is the global attractor for the delay differential equation for all . This has bee…
The Poincaré-Bendixson Theorem and the Non-linear Cauchy-Riemann Equations
J. B. van den Berg, S. Munao, R. C. A. M. Vandervorst
Fiedler and Mallet-Paret prove a version of the classical Poincaré-Bendixson Theorem for scalar parabolic equations. We prove that a similar result holds for bounded solutions of t…