Dissipative Boundary Conditions for Nonlinear 1-D Hyperbolic Systems: Sharp Conditions Through an Approach via Time-Delay Systems

DOI10.1137/140976625zbMath1320.35196arXiv1403.1747OpenAlexW1706515898MaRDI QIDQ5256464

Hoai-Minh Nguyen, Jean-Michel Coron

Publication date: 17 June 2015

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1403.1747

zbMATH Keywords

exponential stabilitycharacteristic method

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Asymptotic stability in control theory (93D20) First-order nonlinear hyperbolic equations (35L60) Initial-boundary value problems for first-order hyperbolic systems (35L50)

Related Items (20)

Boundary feedback stabilization of quasilinear hyperbolic systems with partially dissipative structure ⋮ Dissipative boundary conditions for \(2\times 2\) hyperbolic systems of conservation laws for entropy solutions in BV ⋮ Hautus-Yamamoto criteria for approximate and exact controllability of linear difference delay equations ⋮ Linearized Stability of Partial Differential Equations with Application to Stabilization of the Kuramoto--Sivashinsky Equation ⋮ Lyapunov functions and finite-time stabilization in optimal time for homogeneous linear and quasilinear hyperbolic systems ⋮ Relative Controllability of Linear Difference Equations ⋮ Boundary Exponential Stabilization of 1-Dimensional Inhomogeneous Quasi-Linear Hyperbolic Systems ⋮ Exponential boundary feedback stabilization of a shock steady state for the inviscid Burgers equation ⋮ A quadratic Lyapunov function for Saint-Venant equations with arbitrary friction and space-varying slope ⋮ Exponential stability of density-velocity systems with boundary conditions and source term for the \(H^2\) norm ⋮ Stability of wave networks on elastic and viscoelastic media ⋮ Global exponential stability and input-to-state stability of semilinear hyperbolic systems for the \(L^2\) norm ⋮ Input-to-state stability in sup norms for hyperbolic systems with boundary disturbances ⋮ PREFACE ⋮ Finite Time Stabilization of Nonautonomous First-Order Hyperbolic Systems ⋮ BV Exponential Stability for Systems of Scalar Conservation Laws Using Saturated Controls ⋮ Boundary Stability of 1-D Nonlinear Inhomogeneous Hyperbolic Systems for the $C^{1}$ Norm ⋮ Approximate and exact controllability of linear difference equations ⋮ Sufficient Stability Conditions for Time-varying Networks of Telegrapher's Equations or Difference-Delay Equations ⋮ Contracting differential equations in weighted Banach spaces

Cites Work

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• Exponential Stability and Transfer Functions of Processes Governed by Symmetric Hyperbolic Systems
• Dissipative Boundary Conditions for One-Dimensional Quasi-linear Hyperbolic Systems: Lyapunov Stability for the $C^1$-Norm
• A Strict Lyapunov Function for Boundary Control of Hyperbolic Systems of Conservation Laws

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