last modified: May 2018

  1. Publications ( journal , conference)
    • J. C., Md. Ariful Islam, Scott A. Smolka, Sicun Gao, Radu Grosu,  Tight Continuous-Time Reachtubes for Lagrangian Reachability
      IEEE CDC 2018
      Arxiv link
    • A construction of two different solutions to an elliptic system (with Piotr Boguslaw Mucha)
      Journal of Mathematical Analysis and Applications, 2018, 465(1), 500-530.
      Arxiv link
    • Computer-assisted proof of heteroclinic connections in the one-dimensional Ohta-Kawasaki model ( with T. Wanner )
      SIAM Journal on Applied Dynamical Systems (SIADS), 2018, 17(1), 694 -731.
      Arxiv link
    • J. C. and P. B. Mucha and E. S. Titi and P Zgliczyński,  Stabilizing the Long-time Behavior of the Navier-Stokes Equations and Damped Euler Systems by Fast Oscillating Forces
      Physica D, vol. 369, 2018
      Arxiv link
    • J.C., Md. Ariful Islam, Greg Byrne, Paul Jones, Scott A. Smolka, Radu Grosu,  Lagrangian Reachability
      CAV 2017
      Arxiv link
    • Stabilizing effect of large average initial velocity in forced dissipative PDEs invariant with respect to Galilean transformations (with P. Zgliczyński)
      Journal of Differential Equations, Vol. 261, 8 (2016), pp. 4648-4708
      Arxiv link
    • Existence of globally attracting solutions for one-dimensional viscous Burgers equation with nonautonomous forcing - a computer assisted proof ( with P. Zgliczyński )
      SIAM Journal on Applied Dynamical Systems, 14-2 (2015), pp. 787-821
      Arxiv link
      Click here for software, documentation, numerical data and supplement.
    • Existence of globally attracting fixed points of viscous Burgers equation with constant forcing. A computer assisted proof
      Topological Methods in Nonlinear Analysis, Vol. 45, 2 (2015), 655–697
      Arxiv link
      Click here for software, documentation, numerical data from computer proofs.
    • Efficient and generic algorithm for rigorous integration forward in time of dPDEs: Part I
      Journal of Scientific Computing, Vol. 59, 1 (2014), 28-52
      Download the paper
      Click here for software, documentation, numerical data from tests
      The software used in this paper is reusable. Here I provide a guide

  2. Manuscripts submitted

  3. PhD dissertation
    • Efficient algorithms for rigorous integration forward in time of dPDEs. Existence of globally attracting fixed points of viscous Burgers equation with constant forcing, a computer assisted proof
      PhD dissertation, Jagiellonian University, Krakow, 2013
      Download fulltext
      Click here for supplementary materials

  4. Preprints