We prove the existence of globally attracting solutions of viscous Burgersâ€™ equation with periodic boundary conditions on the interval for some particular choices of viscosity and non-autonomousâ€¦ (More)

The dissertation is divided into two separate parts. First part We propose an e cient and generic algorithm for rigorous integration forward in time of systems of equations originating from partialâ€¦ (More)

We propose an efficient and generic algorithm for rigorous integration forward in time of partial differential equations written in the Fourier basis. By rigorous integration we mean a procedureâ€¦ (More)

We introduce LRT, a new Lagrangian-based ReachTube computation algorithm that conservatively approximates the set of reachable states of a nonlinear dynamical system. LRT makes use of theâ€¦ (More)

We introduce continuous Lagrangian reachability (CLRT), a new algorithm for the computation of a tight and continuous-time reachtube for the solution flows of a nonlinear, time-variant dynamicalâ€¦ (More)

The relationship between the so-called ancient (backwards) solutions to the Navier-Stokes equations in the space or in a half space and the global well-posedness of initial boundary value problemsâ€¦ (More)

We present a computer-assisted proof of heteroclinic connections in the one-dimensional Ohta-Kawasaki model of diblock copolymers. The model is a fourth-order parabolic partial differential equationâ€¦ (More)

In this paper, we survey recent progress in CyberCardia project, a CPS Frontier project funded by the National Science Foundation. The CyberCardia project will lead to significant advances in theâ€¦ (More)