Uniqueness and stability of L∞ solutions for Temple class systems with boundary and properties of the attainable sets

W consider the initial-boundary value problem for a strictly hyperbolic, genuinely nonlinear, Temple class system of conservation laws u(t) + f(u)(x) = 0, u is an element of R-n, on the domain Omega = {(t,x) is an element of R-2 : t greater than or equal to 0, x greater than or equal to 0}. For a class of initial data (u) over bar is an element of L-infinity(R+) and boundary data (u) over tilde is an element of L-infinity(R+) with possibly unbounded variation, we construct a flow of solutions ((u) over bar, (u) over tilde) --> u(t) (=) over dot E-t((u) over bar, (u) over tilde) that depend continuously, in the L-1 distance, both on the initial data and on the boundary data. Moreover, we show that each trajectory t bar right arrow E-t((u) over bar, (u) over tilde) provides the unique weak solution of the corresponding initial-boundary value problem that satisfies an entropy condition of Oleinik type. Next, we study the initial-boundary value problem for the above equation from the point of view of control theory taking the initial data (u) over bar fixed and considering, in connection with a prescribed set U of boundary data regarded as admissible controls, the set of attainable profiles at a fixed time T > 0, and at a fixed point (x) over bar > 0: A(T, U) (=) over dot {E-T((u) over bar, (u) over tilde) (.) ; (u) over tilde is an element of U}, A((x) over bar ,U) (=) overdot {E(.)((u) over bar, (u) over tilde) ; (u) over tilde is an element of U}. We establish closure and compactness of the sets A (T, U), A ((x) over bar, U) in th L-loc(1) topology for a class U of admissible controls satisfying convex constraints.