On sequences of measure-valued solutions of a first-order quasilinear equation

The behavior of bounded sequences of measure-valued solutions of the equation
$$ \operatorname{div}_x \varphi (x,u)+\psi (x,u)=0 $$
is investigated, where $u = u(x)$, $x=(x_1,\dots,x_n)\in\Omega$, and $\Omega\subset\mathbb{R}^n$ is an open set. The main result here is a proof that a bounded sequence of measure-valued solutions of such equations is precompact in the topology of strong convergence.