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

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.

### MSC:

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

### Keywords:

transport equation; BV vector fields; Cauchy problem
Full Text:

### References:

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