Partial Differential Equations and Group Theory: New Perspectives for Applications
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Dordrecht
Springer Netherlands
1994
|
| Series: | Mathematics and Its Applications
293 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | Ordinary differential control theory (the classical theory) studies input/output relations defined by systems of ordinary differential equations (ODE). The various concepts that can be introduced (controllability, observability, invertibility, etc. ) must be tested on formal objects (matrices, vector fields, etc. ) by means of formal operations (multiplication, bracket, rank, etc. ), but without appealing to the explicit integration (search for trajectories, etc. ) of the given ODE. Many partial results have been recently unified by means of new formal methods coming from differential geometry and differential algebra. However, certain problems (invariance, equivalence, linearization, etc. ) naturally lead to systems of partial differential equations (PDE). More generally, partial differential control theory studies input/output relations defined by systems of PDE (mechanics, thermodynamics, hydrodynamics, plasma physics, robotics, etc. ). One of the aims of this book is to extend the preceding concepts to this new situation, where, of course, functional analysis and/or a dynamical system approach cannot be used. A link will be exhibited between this domain of applied mathematics and the famous 'Backlund problem', existing in the study of solitary waves or solitons. In particular, we shall show how the methods of differential elimination presented here will allow us to determine compatibility conditions on input and/or output as a better understanding of the foundations of control theory. At the same time we shall unify differential geometry and differential algebra in a new framework, called differential algebraic geometry |
| Physical Description: | 1 Online-Ressource (X, 478 p) |
| ISBN: | 9789401725392 9789048144327 |
| DOI: | 10.1007/978-94-017-2539-2 |
Staff View
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| isbn | 9789401725392 9789048144327 |
| language | English |
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| spelling | Pommaret, J.-F. Verfasser aut Partial Differential Equations and Group Theory New Perspectives for Applications by J.-F. Pommaret Dordrecht Springer Netherlands 1994 1 Online-Ressource (X, 478 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 293 Ordinary differential control theory (the classical theory) studies input/output relations defined by systems of ordinary differential equations (ODE). The various concepts that can be introduced (controllability, observability, invertibility, etc. ) must be tested on formal objects (matrices, vector fields, etc. ) by means of formal operations (multiplication, bracket, rank, etc. ), but without appealing to the explicit integration (search for trajectories, etc. ) of the given ODE. Many partial results have been recently unified by means of new formal methods coming from differential geometry and differential algebra. However, certain problems (invariance, equivalence, linearization, etc. ) naturally lead to systems of partial differential equations (PDE). More generally, partial differential control theory studies input/output relations defined by systems of PDE (mechanics, thermodynamics, hydrodynamics, plasma physics, robotics, etc. ). One of the aims of this book is to extend the preceding concepts to this new situation, where, of course, functional analysis and/or a dynamical system approach cannot be used. A link will be exhibited between this domain of applied mathematics and the famous 'Backlund problem', existing in the study of solitary waves or solitons. In particular, we shall show how the methods of differential elimination presented here will allow us to determine compatibility conditions on input and/or output as a better understanding of the foundations of control theory. At the same time we shall unify differential geometry and differential algebra in a new framework, called differential algebraic geometry Mathematics Group theory Systems theory Global differential geometry Thermodynamics Differential Geometry Group Theory and Generalizations Theoretical, Mathematical and Computational Physics Systems Theory, Control Mathematik Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Gruppe Mathematik (DE-588)4022379-6 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 s Gruppe Mathematik (DE-588)4022379-6 s 1\p DE-604 Mathematics and Its Applications 293 (DE-604)BV008163334 293 https://doi.org/10.1007/978-94-017-2539-2 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Pommaret, J.-F Partial Differential Equations and Group Theory New Perspectives for Applications Mathematics and Its Applications Mathematics Group theory Systems theory Global differential geometry Thermodynamics Differential Geometry Group Theory and Generalizations Theoretical, Mathematical and Computational Physics Systems Theory, Control Mathematik Partielle Differentialgleichung (DE-588)4044779-0 gnd Gruppe Mathematik (DE-588)4022379-6 gnd |
| subject_GND | (DE-588)4044779-0 (DE-588)4022379-6 |
| title | Partial Differential Equations and Group Theory New Perspectives for Applications |
| title_auth | Partial Differential Equations and Group Theory New Perspectives for Applications |
| title_exact_search | Partial Differential Equations and Group Theory New Perspectives for Applications |
| title_full | Partial Differential Equations and Group Theory New Perspectives for Applications by J.-F. Pommaret |
| title_fullStr | Partial Differential Equations and Group Theory New Perspectives for Applications by J.-F. Pommaret |
| title_full_unstemmed | Partial Differential Equations and Group Theory New Perspectives for Applications by J.-F. Pommaret |
| title_short | Partial Differential Equations and Group Theory |
| title_sort | partial differential equations and group theory new perspectives for applications |
| title_sub | New Perspectives for Applications |
| topic | Mathematics Group theory Systems theory Global differential geometry Thermodynamics Differential Geometry Group Theory and Generalizations Theoretical, Mathematical and Computational Physics Systems Theory, Control Mathematik Partielle Differentialgleichung (DE-588)4044779-0 gnd Gruppe Mathematik (DE-588)4022379-6 gnd |
| topic_facet | Mathematics Group theory Systems theory Global differential geometry Thermodynamics Differential Geometry Group Theory and Generalizations Theoretical, Mathematical and Computational Physics Systems Theory, Control Mathematik Partielle Differentialgleichung Gruppe Mathematik |
| url | https://doi.org/10.1007/978-94-017-2539-2 |
| volume_link | (DE-604)BV008163334 |
| work_keys_str_mv | AT pommaretjf partialdifferentialequationsandgrouptheorynewperspectivesforapplications |