LAUSR

Abstract In this paper, we establish the well-posedness of the following system of two transport equations coupled with a diffusion equation: ∂ t μ t 1 + ∇ ⋅ ( v 1 [ μ t ] μ t 1 ) = N 1 ( t , μ t ) , ∂ t μ t 2 − Δ μ t 2 = N 2 ( t , μ t ) , ∂ t μ t 3 + ∇ ⋅ ( v 2 [ μ t ] μ t 3 ) = N 3 ( t , μ t ) , in R d where μ t 1 , μ t 2 , μ t 3 are finite signed measures. Here, the vector field v 1 , v 2 and the source term N 1 , N 2 , N 3 depend on the measure-valued solution vector μ t = ( μ t 1 , μ t 2 , μ t 3 ) .