Uniqueness and sharp estimates on solutions to hyperbolic systems with dissipative source
Date
2006Source
Communications in Partial Differential EquationsVolume
31Issue
12Pages
1825-1839Google Scholar check
Keyword(s):
Metadata
Show full item recordAbstract
Global weak solutions of a strictly hyperbolic system of balance laws in one-space dimension were constructed (cf. Christoforou, 2006) via the vanishing viscosity method under the assumption that the source term g is dissipative. In this article, we establish sharp estimates on the uniformly Lipschitz semigroup ℘ generated by the vanishing viscosity limit in the general case which includes also nonconservative systems. Furthermore, we prove uniqueness of solutions by means of local integral estimates and show that every "viscosity solution" can be constructed as a limit of vanishing viscosity approximations. Copyright © Taylor & Francis Group, LLC.