In this paper, we examine the stability problem for viscous shock solutions of the isentropic compressible Navier–Stokes equations, or p-system with real viscosity. We first revisit the work of Matsumura and Nishihara, extending the known parameter regime for which small-amplitude viscous shocks are provably spectrally stable by an optimized version of… (More)
This paper presents a constrained backpropagation (CPROP) methodology for solving nonlinear elliptic and parabolic partial differential equations (PDEs) adaptively, subject to changes in the PDE parameters or external forcing. Unlike existing methods based on penalty functions or Lagrange multipliers, CPROP solves the constrained optimization problem… (More)
— This paper considers the problem of computing optimal state and control trajectories for a multiscale dynamical system comprised of many interacting dynamical systems, or agents. A generalized reduced gradient (GRG) approach is presented for distributed optimal control (DOC) problems in which the agent dynamics are described by a small system of… (More)
We announce recent results obtained through a combination of asymptotic ODE estimates and numerical Evans function calculations, which together yield stability of isentropic Navier–Stokes shocks for a γ-law gas with 1 ≤ γ ≤ [1, 2.5]. Other γ may be treated similarly.