  Motivated by porous medium equations with randomly perturbed velocity field,
this paper considers a class of nonlinear degenerate diffusion equations with
nonlinear conservative noise in bounded domains. The existence, uniqueness and
$L_{1}$-stability of non-negative entropy solutions under the homogeneous
Dirichlet boundary condition are proved. The approach combines Kruzhkov's
doubling variables technique with a revised strong entropy condition that is
automatically satisfied by the solutions of approximate equations.
