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
2022

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.
Applied Mathematical Problems in Geophysics
978-3-031-05320-7
978-3-031-05321-4
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11589/241881
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