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Regularity Theory for Hyperbolic PDEs
2021In this chapter we study linear hyperbolic equations (6.1.1) of second order on special Lipschitz domains according to Definition 2.1.8. For these kinds of equations regularity estimates in Kondratiev spaces were derived in which enable us to treat these equations in a similar way as the parabolic problems in Chap. 5.
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Feedback control of hyperbolic PDE systems
AIChE Journal, 1996AbstractThis article deals with distributed parameter systems described by first‐order hyperbolic partial differential equations (PDEs), for which the manipulated input, the controlled output, and the measured output are distributed in space. For these systems, a general output‐feedback control methodology is developed employing a combination of theory
Panagiotis D. Christofides +1 more
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Robust control of hyperbolic PDE systems
Chemical Engineering Science, 1998In the previous chapter, we addressed the control of hyperbolic PDE systems without accounting explicitly for the presence of uncertainty (i.e., presence of mismatch between the model used for controller design and the actual process model) in the design of the controller. This chapter focuses on systems of quasi-linear first-order hyperbolic PDEs with
Panagiotis D. Christofides +1 more
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Feedback Control of Hyperbolic PDE Systems
IFAC Proceedings Volumes, 2000Abstract Many industrial processes are distributed parameter systems (DPS) that can be described by hyperbolic partial differential equations (e.g., some fixed-bed reactors, sheet-forming and fibre-forming processes). Conventionally, the control schemes for these systems have been designed by approximating the original PDEs as a finite number of ...
Huilan Shang +2 more
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Control Methods in Hyperbolic PDEs
Oberwolfach ReportsControl of hyperbolic partial differential equations (PDEs) is a truly interdisciplinary area of research in applied mathematics nurtured by challenging problems arising in most modern applications ranging from road traffic, gas pipeline management, blood circulation, to opinion dynamics and socio-economical models, as well as in environmental and ...
Fabio Ancona +3 more
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Existence/Uniqueness Results for Hyperbolic PDEs
2018The chapter provides a variety of existence and uniqueness results for a single 1 − D, first-order, hyperbolic PDEs, which is in feedback interconnection with a system of ODEs. The results are developed for various cases, some of which are not frequently encountered in the literature: Nonlinear and non-local terms as well as distributed and boundary ...
Iasson Karafyllis, Miroslav Krstic
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Overview of Elliptic–Hyperbolic PDE
2015The variety and broad applicability of elliptic–hyperbolic equations are illustrated. Included are brief discussions of: the essentials and history of equation type; a “zoo” of elliptic–hyperbolic equations; systems of elliptic–hyperbolic equations; a quasilinear example having multiple sonic lines, with an application to a recent problem in geometry ...
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Finite Difference Methods for Hyperbolic PDEs
2015This self-contained chapter focuses on finite difference approximation of hyperbolic boundary value problems. A number of explicit and implicit time-stepping schemes are introduced and their stability, dissipation and dispersion is analysed. State-of-the-art schemes for hyperbolic PDEs that involve flux limiters are discussed at the end of the chapter.
David F. Griffiths +2 more
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