Consider the Cauchy problem for a hyperbolic n × n system of conservation laws in one space dimension: ut + f(u)cursive Greek chi = 0, u(0, cursive Greek chi) = ū(cursive Greek chi). (CP) Relying on the existence of a continuous semigroup of solutions, we prove that the entropy admissible solution of (CP) is unique within the class of functions u = u(t, cursive Greek chi) which have bounded variation along a suitable family of space-like curves.
All Science Journal Classification (ASJC) codes
- Discrete Mathematics and Combinatorics
- Applied Mathematics