A chain rule formula in the space \(BV\) and applications to conservation laws. (English) Zbl 1229.26020
A new chain rule formula is shown for the distributional derivative of the composite function \(v(x)=B(x,u(x))\), where \(u: (a,b) \to\mathbb R^n\) has bounded variation, \(B(x,.)\) is continuously differentiable and \(B(., u)\) has bounded variation. Applications of this formula are shown in order to deal with the discontinuous flux appearing in conservation laws in one space variable.
Reviewer: Vladimír Janiš (Banská Bystrica)
MSC:
26A45 | Functions of bounded variation, generalizations |
35L65 | Hyperbolic conservation laws |
26A24 | Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems |
46F10 | Operations with distributions and generalized functions |