Uniqueness of continuous solutions for BV vector fields
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.
scientific article; zbMATH DE number 1820876