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We give a new perspective on the existence of viscosity solutions for a stationary and a time-dependent first-order Hamilton-Jacobi equation. Following recent comparison principles, we work in a framework in which we consider a subsolution…

Analysis of PDEs · Mathematics 2025-11-25 Serena Della Corte , Richard C. Kraaij

This paper establishes the equivalence between systems described by a single first-order hyperbolic partial differential equation and systems described by integral delay equations. System-theoretic results are provided for both classes of…

Optimization and Control · Mathematics 2019-02-20 Iasson Karafyllis , Miroslav Krstic

Some of the guiding problems in partially hyperbolic systems are the following: (1) Examples, (2) Properties of invariant foliations, (3) Accessibility, (4) Ergodicity, (5) Lyapunov exponents, (6) Integrability of central foliations, (7)…

Dynamical Systems · Mathematics 2007-05-23 F. Rodriguez Hertz , M. A. Rodriguez Hertz , R. Ures

In this paper, we study the local exact boundary controllability of entropy solutions to a class linearly degenerate hyperbolic systems of conservation laws with constant multiplicity. The authors prove the two-sided boundary…

Optimization and Control · Mathematics 2016-07-13 Tatsien Li , Lei Yu

This paper is concerned with the existence and the regularity of global solutions to the linear wave equation associated with two-point type boundary conditions. We also investigate the decay properties of the global solutions to this…

Analysis of PDEs · Mathematics 2011-11-29 Le Xuan Truong , Le Thi Phuong Ngoc , Alain Pham Ngoc Dinh , Nguyen Thanh Long

The paper deals with the control and regulation by integral controllers forthe nonlinear systems governed by scalar quasi-linear hyperbolic partial differentialequations. Both the control input and the measured output are located on the…

Analysis of PDEs · Mathematics 2019-04-30 Vincent Andrieu , Ngoc-Tu Trinh , Cheng-Zhong Xu

Hyperexponential stability is investigated for dynamical systems with the use of both, explicit and implicit, Lyapunov function methods. A nonlinear hyperexponential control is designed for stabilizing linear systems. The tuning procedure…

Systems and Control · Electrical Eng. & Systems 2022-07-19 Konstantin Zimenko , Denis Efimov , Andrey Polyakov

We present a frequency domain based $H_\infty$-control strategy to solve boundary control problems for systems governed by parabolic or hyperbolic partial differential equation, where controllers are constrained to be physically…

Optimization and Control · Mathematics 2019-05-17 Pierre Apkarian , Dominikus Noll

We establish a link between stability estimates for a hyperbolic inverse problem via the Boundary Control method and the blowup of a constant appearing in the contexts of optimal unique continuation and cost of approximate controllability.

Analysis of PDEs · Mathematics 2025-03-11 Spyridon Filippas , Lauri Oksanen

A degenerate wave equation with time-varying delay in the boundary control input is considered. The well-posedness of the system is established by applying the semigroup theory. The boundary stabilization of the degenerate wave equation is…

Analysis of PDEs · Mathematics 2024-10-22 Menglan Liao

This paper presents a novel method to synthesize stochastic control Lyapunov functions for a class of nonlinear, stochastic control systems. In this work, the classical nonlinear Hamilton-Jacobi-Bellman partial differential equation is…

Optimization and Control · Mathematics 2016-11-17 Yoke Peng Leong , Matanya B. Horowitz , Joel W. Burdick

Stability of stationary solutions of parabolic equations is conventionally studied by linear stability analysis, Lyapunov functions or lower and upper functions. We discuss here another approach based on differential inequalities written…

Functional Analysis · Mathematics 2012-06-26 A. G. Ramm , V. Volpert

We consider optimal control problems for partial differential equations where the controls take binary values but vary over the time horizon, they can thus be seen as dynamic switches. The switching patterns may be subject to combinatorial…

Optimization and Control · Mathematics 2024-04-04 Christoph Buchheim , Alexandra Grütering , Christian Meyer

For a system that is governed by the isothermal Euler equations with friction for ideal gas, the corresponding field of characteristic curves is determined by the velocity of the flow. This velocity is determined by a second-order…

Optimization and Control · Mathematics 2016-08-09 Martin Gugat , Günter Leugering , Ke Wang

Boundary feedback control design is studied for 1D hyperbolic systems with an in-domain disturbance and a boundary feedback controller under the effect of actuator saturation. Nonlinear semigroup theory is used to prove well-posedness of…

Optimization and Control · Mathematics 2022-05-18 Suha Shreim , Francesco Ferrante , Christophe Prieur

This paper presents a new method for synthesizing stochastic control Lyapunov functions for a class of nonlinear stochastic control systems. The technique relies on a transformation of the classical nonlinear Hamilton-Jacobi-Bellman partial…

Optimization and Control · Mathematics 2017-09-07 Yoke Peng Leong , Matanya B. Horowitz , Joel W. Burdick

This review examines classical and recent results on controllability and inverse problems for hyperbolic and dispersive equations with dynamic boundary conditions. We aim to illustrate the applicability of Carleman estimates to establish…

Optimization and Control · Mathematics 2025-05-22 S. E. Chorfi , L. Maniar , R. Morales

This paper extends our recent results on multi-dimensional discrete-velocity models to the numerical level. By adopting an operator splitting scheme and introducing a suitable discrete Lyapunov function, we derive numerical control laws…

Numerical Analysis · Mathematics 2025-10-21 Haitian Yang , Wen-An Yong

We study hyperbolic systems of one-dimensional partial differential equations under general, possibly non-local boundary conditions. A large class of evolution equations, either on individual 1-dimensional intervals or on general networks,…

Analysis of PDEs · Mathematics 2021-01-19 Marjeta Kramar Fijavž , Delio Mugnolo , Serge Nicaise

This paper is devoted to confront two different approaches to the problem of dynam-ical perfect plasticity. Interpreting this model as a constrained boundary value Friedrichs' system enables one to derive admissible hyperbolic boundary…

Analysis of PDEs · Mathematics 2016-11-23 Jean-Francois Babadjian , Clément Mifsud