In this work, we consider the problem of boundary stabilization for a quasilinear 2 × 2 system of first-order hyperbolic PDEs. We design a new full-state feedback control law, with actuation on only one end of the domain, which achieves H2 exponential stability of the closedloop system. Our proof uses a backstepping transformation to find new variables for which a strict Lyapunov function can b...

In this paper, we construct a conformal scattering theory for Dirac fields in the interior of Reissner–Nordström-like black hole, between hole event horizon and Cauchy horizon. The main result is resolution characteristic problem equation on horizons by solving system wave equations re-interpreting its solution as components required solution.

I. Introduction. Stokes' theorem on a manifold is a central theorem of mathematics. Special cases include the integral theorems of vector analysis and the Cauchy-Goursat theorem. My purpose here is to prove this version of Stokes' Theorem. Let ω be a continuous differential (n − 1)-form on a compact oriented n-manifold M with boundary ∂M. Suppose that ω is differen-tiable on M − ∂M and dω is Le...

For semilinear Gellerstedt equations with Tricomi, Goursat, or Dirichlet boundary conditions, we prove Pohožaev-type identities and derive nonexistence results that exploit an invariance of the linear part with respect to certain nonhomogeneous dilations. A critical-exponent phenomenon of power type in the nonlinearity is exhibited in these mixed elliptic-hyperbolic or degenerate settings where...

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 14 September 2020Accepted: 03 June 2021Published online: 09 2021Keywordskernel, path signature, Goursat PDE, sequential data, geometric rough path, integrationAMS Subject Headings60L10, 60L20Publication DataISSN (online): 2577-0187Publisher: Society for Industrial and App...

In this paper, the method of exterior diflerential systems for analyzing nonlinear systems is presented. Conditions are given for converting Pfafian systems into Goursat normal f o r m , and for converting control systems into Brunovsky form. All of the existing results on feedback linearization for control systems can be restated in the language of Pfafian systems, and in addition, new conditi...