Admissible Solutions of Hyperbolic Conservation Laws

· American Mathematical Society: Memoirs of the American Mathematical Society Ibhuku elingu-240 · American Mathematical Soc.
I-Ebook
78
Amakhasi
Izilinganiso nezibuyekezo aziqinisekisiwe  Funda Kabanzi

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We consider a system of n conservation laws: [partial derivative/boundary/degree of a polynomial symbol]∂u [over] [partial derivative/boundary/degree of a polynomial symbol]∂t + [partial derivative/boundary/degree of a polynomial symbol]∂f(u) [over] [partial derivative/boundary/degree of a polynomial symbol]∂x = 0. The system is assumed to be strictly hyperbolic, but not necessarily genuinely nonlinear in the sense of Peter Lax (Hyperbolic systems of conservation laws, 1957). Our purpose is to study the regularity, large-time behavior and the approximation of the solution of the initial-value problem. Our analysis is based on the random choice method, using the solution of the Riemann problem, as building blocks.

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