Uniqueness of continuous solutions for BV vector fields. (English) Zbl 1017.35029

Colombini, Ferruccio; Lerner, Nicolas

Duke Math. J. 111, No. 2, 357-384 (2002).

The authors study the Cauchy problem for a transport equation \(Xu=cu\) associated with a vector field \(X=\partial_t+\sum_{j=1}^d a_j(t,x)\partial_j\), in which coefficients \(a_j\) are assumed to be functions of bounded variation. Under some additional assumptions on growth of the coefficients the authors prove the uniqueness of continuous solutions.

Reviewer: Evgeniy Panov (Novgorod)

MSC:

35F10	Initial value problems for linear first-order PDEs
26A45	Functions of bounded variation, generalizations

Keywords:

transport equation; BV vector fields; Cauchy problem

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