Summary
A methodology to investigate discontinuity wave propagation in first-order hyperbolic quasi-linear partial differential systems, when the field variables are constrained by algebraic relations, is performed. It is shown that the algebraic constraints among the unknowns are related to differential constraints for the solutions to the field equations or to evolution equations which are linearly dependent on the field wave equations. Hyperbolicity is considered on the manifold of the constrained field variables (constrained hyperbolicity). Several physical examples are analysed in detail.
Riassunto
Si sviluppa una metodologia per studiare la propagazione délie onde di discontinuitá nei sistemi quasi lineari di equazioni alle derivate parziali del primo ordine, nel caso in cui le variabili di oampo sono legate da vinooli algebrioi. Si mostra che i vincoli algebrici fra le variabili di oampo sono correlati con dei vinooli differenziali per le soluzioni delle equazioni di campo evolutive linearmente indipendenti. Si considéra l’iperbolicità sulla varietà delle variabili di oampo vincolate (iperbolicità vinoolata). Si esaminano diversi esempi fisioi in dettaglio.
Резюме
Исследуется распрос транение разрыва непрерывности волны в системах гиперболических ква зи-линейных дифферен циальных уравнений в частных п роизводных первого порядка, когд а полевые переменные ограничены алгебраическими соотношениями. Показ ывается, что алгебраи ческие ограничения, наложен ные на неизвестные, связаны с дифференциальными ограничениями для ре шений полевых уравнениях или в урав нениях эволюции, кото рые линейно зависят от полевых во лновых уравнеий. Гиперболич ность рассматривает ся на множестве ограничен ных полевых переменных (ограниче нная гиперболичност ь). Подробно анализируются некоторые физически е примеры.
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Strumia, A. Wave propagation and symmetric hyperbolic systems of conservation laws with constrained field variables. Nuov Cim B 101, 1–18 (1988). https://doi.org/10.1007/BF02828066
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DOI: https://doi.org/10.1007/BF02828066