Sbv Regularity of Genuinely Nonlinear Hyperbolic Systems of Conservation Laws in One Space Dimension
نویسنده
چکیده
The problem of the presence of Cantor part in the derivative of a solution to a hyperbolic system of conservation laws is considered. An overview of the techniques involved in the proof is given, and a collection of related problems concludes the paper.
منابع مشابه
Sbv Regularity for Genuinely Nonlinear, Strictly Hyperbolic Systems of Conservation Laws in One Space Dimension
We prove that if t 7→ u(t) ∈ BV(R) is the entropy solution to a N × N strictly hyperbolic system of conservation laws with genuinely nonlinear characteristic fields ut + f(u)x = 0, then up to a countable set of times {tn}n∈N the function u(t) is in SBV, i.e. its distributional derivative ux is a measure with no Cantorian part. The proof is based on the decomposition of ux(t) into waves belongin...
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تاریخ انتشار 2011