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2010, ISBN 9780691142869, xiii, 328

... require real-time solution of Riccati or other algebraic operator-valued equations. The book emphasizes stabilization by boundary control and using boundary sensing for unstable PDE systems with an infinite relative degree...

Distributed parameter systems | Differential equations, Parabolic | Adaptive control systems | Mathematics

Distributed parameter systems | Differential equations, Parabolic | Adaptive control systems | Mathematics

Book

2013, 1. Aufl., Communications and control engineering., ISBN 9783642300158, xix, 366

This monograph presents new model-based design methods for trajectory planning, feedback stabilization, state estimation, and tracking control of distributed-parameter systems governed by partial differential equations (PDEs...

Nonlinear control theory | Differential equations, Partial | Distributed parameter systems

Nonlinear control theory | Differential equations, Partial | Distributed parameter systems

Book

Journal of computational physics, ISSN 0021-9991, 08/2012, Volume 231, Issue 20, pp. 6770 - 6789

We give a systematic method for discretizing Hamiltonian partial differential equations (PDEs...

Dissipative PDEs | Hamiltonian PDEs | Time integration | Average vector field method | Physical Sciences | Computer Science, Interdisciplinary Applications | Technology | Physics, Mathematical | Computer Science | Physics | Science & Technology | Methods | Differential equations | Partial differential equations | Mathematical analysis | Dissipation | Preserves | Mathematical models | Schroedinger equation | Preserving | Heat equations | Mathematics - Numerical Analysis

Dissipative PDEs | Hamiltonian PDEs | Time integration | Average vector field method | Physical Sciences | Computer Science, Interdisciplinary Applications | Technology | Physics, Mathematical | Computer Science | Physics | Science & Technology | Methods | Differential equations | Partial differential equations | Mathematical analysis | Dissipation | Preserves | Mathematical models | Schroedinger equation | Preserving | Heat equations | Mathematics - Numerical Analysis

Journal Article

2004, Mathematical notes, ISBN 0691119538, Volume 45, viii, 218

Elliptic equations of critical Sobolev growth have been the target of investigation for decades because they have proved to be of great importance in analysis, geometry, and physics...

Differential equations, Nonlinear | Geometry, Riemannian | Calculus of variations | Differential Equations, Nonlinear | Mathematics | Calculus of Variations | Differential equations, Elliptic

Differential equations, Nonlinear | Geometry, Riemannian | Calculus of variations | Differential Equations, Nonlinear | Mathematics | Calculus of Variations | Differential equations, Elliptic

Book

Acta numerica, ISSN 0962-4929, 05/2015, Volume 24, pp. 1 - 159

Parametrized families of PDEs arise in various contexts such as inverse problems, control and optimization, risk assessment, and uncertainty quantification...

Physical Sciences | Mathematics | Science & Technology | Partial differential equations | Parameter estimation | Approximations | Numerical Analysis

Physical Sciences | Mathematics | Science & Technology | Partial differential equations | Parameter estimation | Approximations | Numerical Analysis

Journal Article

11/2018, SEMA SIMAI Springer Series, ISBN 9783319976129, Volume 17, 249

This book contains the main results of the talks given at the workshop "Recent Advances in PDEs...

Mathematics | Mathematical Modeling and Industrial Mathematics | Mathematics and Statistics | Numerical Analysis | Partial Differential Equations

Mathematics | Mathematical Modeling and Industrial Mathematics | Mathematics and Statistics | Numerical Analysis | Partial Differential Equations

eBook

2018, SEMA SIMAI Springer Series, ISBN 9783319946757, Volume 15, 323

This volume gathers contributions from participants of the Introductory School and the IHP thematic quarter on Numerical Methods for PDE, held in 2016 in Cargese (Corsica...

Differential equations, Partial-Asymptotic theory | Mathematics | Computational Science and Engineering | Mathematics and Statistics | Numerical Analysis | Partial Differential Equations

Differential equations, Partial-Asymptotic theory | Mathematics | Computational Science and Engineering | Mathematics and Statistics | Numerical Analysis | Partial Differential Equations

eBook

8.
Full Text
Control of Homodirectional and General Heterodirectional Linear Coupled Hyperbolic PDEs

IEEE transactions on automatic control, ISSN 1558-2523, 11/2016, Volume 61, Issue 11, pp. 3301 - 3314

Research on stabilization of coupled hyperbolic PDEs has been dominated by the focus on pairs of counter-convecting ("heterodirectional...

Couplings | general coupled hyperbolic system | Backstepping | boundary observer | Boundary conditions | Trajectory | Mathematical model | Kernel | boundary control | trajectory tracking | Engineering, Electrical & Electronic | Engineering | Automation & Control Systems | Technology | Science & Technology | Linear systems | Usage | Mathematical models | Stability | Research | Stabilization | Tracking problem | Automatic control | Control systems | Coupling | Boundaries | Transport | Output feedback | Computer Science

Couplings | general coupled hyperbolic system | Backstepping | boundary observer | Boundary conditions | Trajectory | Mathematical model | Kernel | boundary control | trajectory tracking | Engineering, Electrical & Electronic | Engineering | Automation & Control Systems | Technology | Science & Technology | Linear systems | Usage | Mathematical models | Stability | Research | Stabilization | Tracking problem | Automatic control | Control systems | Coupling | Boundaries | Transport | Output feedback | Computer Science

Journal Article

Automatica (Oxford), ISSN 0005-1098, 01/2018, Volume 87, pp. 281 - 289

We solve the problem of stabilizing a linear ODE having a system of a linearly coupled hyperbolic PDEs in the actuating path...

Predictor feedback | Stabilization | Distributed parameter systems | Hyperbolic systems | Engineering, Electrical & Electronic | Engineering | Automation & Control Systems | Technology | Science & Technology | Analysis of PDEs | Computer Science | Systems and Control | Mathematics | Automatic Control Engineering | Optimization and Control | Engineering Sciences | Automatic

Predictor feedback | Stabilization | Distributed parameter systems | Hyperbolic systems | Engineering, Electrical & Electronic | Engineering | Automation & Control Systems | Technology | Science & Technology | Analysis of PDEs | Computer Science | Systems and Control | Mathematics | Automatic Control Engineering | Optimization and Control | Engineering Sciences | Automatic

Journal Article

Inverse problems, ISSN 1361-6420, 08/2019, Volume 35, Issue 8, p. 084003

Very recently Warma (2019 SIAM J. Control Optim. to appear) has shown that for nonlocal PDEs associated with the fractional Laplacian, the classical notion...

Physical Sciences | Mathematics | Mathematics, Applied | Physics | Physics, Mathematical | Science & Technology

Physical Sciences | Mathematics | Mathematics, Applied | Physics | Physics, Mathematical | Science & Technology

Journal Article

2015, 2015, Atlantis Studies in Differential Equations, ISBN 9462391114, Volume 4, 417

This monograph offers the reader a treatment of the theory of evolution PDEs with nonstandard growth conditions...

Quasilinearization | Differential equations, Hyperbolic | Differential equations, Parabolic | Mathematics | Functional Analysis | Mathematics and Statistics | Partial Differential Equations | Differential equations, Partial | Evolution equations

Quasilinearization | Differential equations, Hyperbolic | Differential equations, Parabolic | Mathematics | Functional Analysis | Mathematics and Statistics | Partial Differential Equations | Differential equations, Partial | Evolution equations

eBook

The Annals of probability, ISSN 0091-1798, 01/2014, Volume 42, Issue 1, pp. 204 - 236

In this paper we propose a notion of viscosity solutions for path dependent semi-linear parabolic PDEs...

Viscosity | Partial differential equations | Uniqueness | Differential equations | Mathematics | Mathematical vectors | Path dependence | Random variables | Coefficients | Stopping distances | Comparison principle | Path dependent PDEs | Backward SDEs | Functional itô formula | Viscosity solutions | Statistics & Probability | Physical Sciences | Science & Technology | Mathematical problems | Studies | Calculus | Parabolas | Markov analysis | 60H10 | 60H30 | 35D40 | viscosity solutions | backward SDEs | functional Itô formula | comparison principle | 35K10

Viscosity | Partial differential equations | Uniqueness | Differential equations | Mathematics | Mathematical vectors | Path dependence | Random variables | Coefficients | Stopping distances | Comparison principle | Path dependent PDEs | Backward SDEs | Functional itô formula | Viscosity solutions | Statistics & Probability | Physical Sciences | Science & Technology | Mathematical problems | Studies | Calculus | Parabolas | Markov analysis | 60H10 | 60H30 | 35D40 | viscosity solutions | backward SDEs | functional Itô formula | comparison principle | 35K10

Journal Article

09/2018, Lecture Notes in Mathematics, ISBN 3319949101, Volume 2219

eBook

Journal of computational physics, ISSN 0021-9991, 12/2019, Volume 399, p. 108925

Partial differential equations (PDEs) are commonly derived based on empirical observations...

Dynamic system | Partial differential equations | Convolutional neural network | Symbolic neural network | Physical Sciences | Computer Science, Interdisciplinary Applications | Technology | Physics, Mathematical | Computer Science | Physics | Science & Technology | Learning | Operators (mathematics) | Time dependence | Multilayers | Neural networks | Empirical equations | Artificial neural networks | Mathematical models | Nonlinear response | Response functions

Dynamic system | Partial differential equations | Convolutional neural network | Symbolic neural network | Physical Sciences | Computer Science, Interdisciplinary Applications | Technology | Physics, Mathematical | Computer Science | Physics | Science & Technology | Learning | Operators (mathematics) | Time dependence | Multilayers | Neural networks | Empirical equations | Artificial neural networks | Mathematical models | Nonlinear response | Response functions

Journal Article