... ukk≤ ε ϕεon D and so 0 ≤ u1≤ ε ϕεon D. Thereby, the continuity of ϕε in every dense point of the boundary of D and the arbitrariness of ε guarantee thatu1∈ C0D.Finally, we will ... study of gas dynamics and fluids mechanics, and in the study of relativisticmechanics, nuclear physics, and chemically reacting system see, e.g., 1 and the referencestherein for the continuous ... on the boundary of D,andCcD is the set of all continuousfunctions on D with compact support on a, bT. We denote as ·CD the norm in CD,thatis, the supremum norm.On the other hand,...