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Record Nr. |
UNISALENTO991002946249707536 |
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Autore |
Robertz, Daniel |
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Titolo |
Formal algorithmic elimination for PDEs / Daniel Robertz |
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Pubbl/distr/stampa |
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Cham [Switzerland] : Springer, c2014 |
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ISBN |
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Descrizione fisica |
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vi, 283 p. ; ill. ; 24 cm |
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Collana |
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Lecture notes in mathematics, 0075-8434 ; 2121 |
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Classificazione |
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AMS 12H05 |
AMS 13P10 |
AMS 16S36 |
AMS 35-02 |
LC QA192.R62 |
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Disciplina |
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Soggetti |
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Differential equations, Partial |
Elimination |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di bibliografia |
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Includes bibliographical references and index |
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Nota di contenuto |
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Introduction ; Formal methods for PDE systems ; Differential elimination for analytic functions ; Basic principles and supplementary material ; References ; List of algorithms ; List of examples ; Index of notation ; Index |
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Sommario/riassunto |
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Investigating the correspondence between systems of partial differential equations and their analytic solutions using a formal approach, this monograph presents algorithms to determine the set of analytic solutions of such a system and conversely to find differential equations whose set of solutions coincides with a given parametrized set of analytic functions. After giving a detailed introduction to Janet bases and Thomas decomposition, the problem of finding an implicit description of certain sets of analytic functions in terms of differential equations is addressed. Effective methods of varying generality are developed to solve the differential elimination problems that arise in this context. In particular, it is demonstrated how the symbolic solution of partial differential equations profits from the study of the implicitization problem. For instance, certain families of exact solutions of the Navier-Stokes equations can be computed |
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