Abstract: Consider the initial-boundary value problem for a strictly hyperbolic, genuinely nonlinear, Temple class system of conservation laws
ut+f(u)x=0, u(0,x)= u0(x), u(t,a)= ua(t), u(t,b)= ub(t), (1)on the domain \Omega = {(t,x) in R2 : t >= 0, a <= x <= b}. We study the mixed problem (1) from the point of view of control theory, taking the initial data u0 fixed, and regarding the boundary data ua, ub as control functions that vary in prescribed sets Ua, Ub, of Linf boundary controls. In particular, we consider the family of configurationsA(T) = { u(T,.); u is a solution to (1), ua in Ua, ub in Ub }that can be attained by the system at a given time T>0, and we give a description of the attainable set A(T) in terms of suitable Oleinik-type conditions. We also establish closure and compactness of the set A(T) in the L1 topology.
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