Abstract:Consider the initial-boundary value problem for a strictly hyperbolic, genuinely nonlinear, Temple class system of conservation lawsuon the domain \Omega = {(t,x) in R_{t}+f(u)_{x}=0, u(0,x)= u_{0}(x), u(t,a)= u_{a}(t), u(t,b)= u_{b}(t), (1)^{2}: t >= 0, a <= x <= b}. We study the mixed problem (1) from the point of view of control theory, taking the initial data u_{0}fixed, and regarding the boundary data u_{a}, u_{b}as control functions that vary in prescribed sets U_{a}, U_{b}, of L^{inf}boundary controls. In particular, we consider the family of configurationsA(T) = { u(T,.); u is a solution to (1), uthat 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 L_{a}in U_{a}, u_{b}in U_{b}}^{1}topology.

**Paper:**- Available as PostScript (410 Kbytes) or gzipped PostScript (145 Kbytes; uncompress using gunzip).
**Author(s):**- Fabio Ancona<, <ancona@ciram3.ing.unibo.it>
- Giuseppe Maria Coclite, <coclite@sissa.it>
**Publishing information:****Comments:****Submitted by:**- <coclite@sissa.it> May 15 2002.

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