Minimal entropy conditions for Burgers equation
نویسندگان
چکیده
منابع مشابه
Minimal Entropy Conditions for Burgers Equation
We consider a scalar conservation law in one space dimension with strictly convex flux f ∈ C(R) ut + f(u)x = 0 for (t, x) ∈ [0,∞) × R (1) and initial data u(0, ·) = u0 ∈ L (R). It is well–known that, even for smooth initial data, the solution of (1) ceases to exist in the classical sense due to the formation of shocks in finite time (cf. Riemann 1859 [10]). Therefore one has to consider weak so...
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This document provides a proof that the solutions to the convectively filtered Burgers equation, will converge to the entropy solution of the inviscid Burgers equation when certain restrictions are put on the initial conditions. It does so by first establishing convergence to a weak solution of the inviscid Burgers equation and then showing that the weak solution is the entropy solution. Then t...
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ژورنال
عنوان ژورنال: Quarterly of Applied Mathematics
سال: 2004
ISSN: 0033-569X,1552-4485
DOI: 10.1090/qam/2104269