A general fundamental mathematical framework at the base of the conservation laws of continuum mechanics is introduced. The notions of weak solutions, and the issues related to the entropy criteria are discussed in detail. The spontaneous creation of singularities, and the occurrence of diffusive limits are explained in view of their physical implications. A particular emphasis is given to the applications of hyperbolic conservation laws in the models of gas dynamics, nonlinear elasticity and traffic flows.
Conservation Laws in Continuum Mechanics / Coclite, Giuseppe Maria; Maddalena, Francesco (LECTURE NOTES IN MATHEMATICS). - In: Applied Mathematical Problems in Geophysics / [a cura di] M. Chiappini, V. Vespri. - STAMPA. - [s.l], 2022. - ISBN 978-3-031-05320-7. - pp. 157-207 [10.1007/978-3-031-05321-4_6]
Conservation Laws in Continuum Mechanics
Coclite, Giuseppe Maria
;Maddalena, Francesco
2022-01-01
Abstract
A general fundamental mathematical framework at the base of the conservation laws of continuum mechanics is introduced. The notions of weak solutions, and the issues related to the entropy criteria are discussed in detail. The spontaneous creation of singularities, and the occurrence of diffusive limits are explained in view of their physical implications. A particular emphasis is given to the applications of hyperbolic conservation laws in the models of gas dynamics, nonlinear elasticity and traffic flows.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
