We establish the existence and uniqueness of weak solutions to the parabolic system with nonstandard growth condition and cross diffusion, ∂tu−diva(x, t,∇u

In section 3, we shall introduce the admissibility concept for solutions of the original system (1), and prove existence and uniqueness of a solution to the Riemann problem in

In the aforementioned work, the existence of weak solutions is established under two strict model assumptions: (i) the coupling term in the fluid flow equation is linear; and (ii)

uniqueness, distributional solutions, nonlinear degenerate diffusion, porous medium equation, Stefan problem, fractional Laplacian, nonlocal operators, existence, stability,