A uniqueness condition for hyperbolic systems of conservation laws
نویسندگان
چکیده
منابع مشابه
A Uniqueness Condition for Hyperbolic Systems of Conservation Laws
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) = ū(x). (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, x) which have bounded variation along a suitable family of space-like curves.
متن کاملHyperbolic Systems of Conservation Laws
Conservation laws are first order systems of quasilinear partial differential equations in divergence form; they express the balance laws of continuum physics for media with "elastic" response, in which internal dissipation is neglected. The absence of internal dissipation is manifested in the emergence of solutions with jump discontinuities across manifolds of codimension one, representing, in...
متن کاملHyperbolic Systems of Conservation Laws
Its purpose is to provide an account of some recent advances in the mathematical theory of hyperbolic systems of conservation laws in one space dimension. After a brief review of basic concepts, we describe in detail the method of wave-front tracking approximation and present some of the latest results on uniqueness and stability of entropy weak solutions. 1-Review of basic theory. This chapter...
متن کاملSystems of Hyperbolic Conservation Laws with Memory
Global weak solutions of bounded variation to systems of balance laws with non-local source are constructed by the method of vanishing viscosity. Suitable dissipativeness assumptions are imposed on the source terms to assure convergence of the method. Under these hypotheses, the total variation remains uniformly bounded and integrable in time, the vanishing viscosity solutions are uniformly sta...
متن کاملUniqueness via the Adjoint Problem for Systems of Conservation Laws
We prove a result of uniqueness of the entropy weak solution to the Cauchy problem for a class of nonlinear hyperbolic systems of conservation laws, that includes in particular the p-system of isentropic gas dynamics. Our result concerns weak solutions satisfying the, as we call it, Wave Entropy Condition or WEC, for short, introduced in this paper. The main feature of this condition is that it...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete and Continuous Dynamical Systems
سال: 2000
ISSN: 1078-0947
DOI: 10.3934/dcds.2000.6.673