Oxford University Press, USA 2006. - 536 pages.
Hyperbolic Partial Differential Equations(PDEs), and in particular first-order systems of conservation laws, have been a fashionable topic for over half a century. Many book shave been written, but few of them deal with genuinely multidimensional hyperbolic problems: in this respect the most classical, though not so well-known, references are the books by Reiko Sakamoto, by Jacques
Chazarain and Alain Piriou, and by Andrew Majda. Quoting Majda from his 1984 book, the rigorous theory of multi-D conservation laws is a field in its infancy. We dare say it is still the case today. However, some advance shave been made by various authors. To speak only of the stability of shock waves, we may think in particular of: M'etivier and coworkers, who continued Majda’s work in several interesting directions – weak shocks, lessening there gularity of the data, elucidation of the ‘blockstructure’ assumption in the case of characteristics with constant multiplicities (we shall speak here of constantly hyperbolic operators).
Hyperbolic Partial Differential Equations(PDEs), and in particular first-order systems of conservation laws, have been a fashionable topic for over half a century. Many book shave been written, but few of them deal with genuinely multidimensional hyperbolic problems: in this respect the most classical, though not so well-known, references are the books by Reiko Sakamoto, by Jacques
Chazarain and Alain Piriou, and by Andrew Majda. Quoting Majda from his 1984 book, the rigorous theory of multi-D conservation laws is a field in its infancy. We dare say it is still the case today. However, some advance shave been made by various authors. To speak only of the stability of shock waves, we may think in particular of: M'etivier and coworkers, who continued Majda’s work in several interesting directions – weak shocks, lessening there gularity of the data, elucidation of the ‘blockstructure’ assumption in the case of characteristics with constant multiplicities (we shall speak here of constantly hyperbolic operators).