A uniqueness condition for hyperbolic systems of conservation laws | Zendy

Marta Lewicka | Zendy; Alberto Bressan | Zendy

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A uniqueness condition for hyperbolic systems of conservation laws

Author(s) -

Marta Lewicka,

Alberto Bressan

Publication year - 2000

Publication title -

discrete and continuous dynamical systems

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.289

H-Index - 70

eISSN - 1553-5231

pISSN - 1078-0947

DOI - 10.3934/dcds.2000.6.673

Subject(s) - conservation law , uniqueness , semigroup , bounded function , mathematics , bounded variation , pure mathematics , entropy (arrow of time) , class (philosophy) , cauchy problem , initial value problem , hyperbolic partial differential equation , mathematical analysis , physics , partial differential equation , computer science , quantum mechanics , artificial intelligence

Consider the Cauchy problem for a hyperbolic n × n system of conservation laws in one space dimension: ut + f(u)x = 0, u(0,x) = ¯ u(x). (CP) Relying on the existence of a continuous semigroup of solutions, we prove that the entropy ad- missible solution of (CP) is unique within the class of functions u = u(t,x) which have bounded variation along a suitable family of space-like curves.

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