@article {2005,
title = {On the attainable set for Temple class systems with boundary controls},
journal = {SIAM J. Control Optim. 43 (2005) 2166-2190},
number = {SISSA;10/2002/M},
year = {2005},
publisher = {SISSA Library},
abstract = {Consider the initial-boundary value problem for a strictly hyperbolic, genuinely nonlinear, Temple class system of conservation laws \% $$ u_t+f(u)_x=0, \\\\qquad u(0,x)=\\\\ov u(x), \\\\qquad {{array}{ll} \&u(t,a)=\\\\widetilde u_a(t), \\\\noalign{\\\\smallskip} \&u(t,b)=\\\\widetilde u_b(t), {array}. \\\\eqno(1) $$ on the domain $\\\\Omega =\\\\{(t,x)\\\\in\\\\R^2 : t\\\\geq 0, a \\\\le x\\\\leq b\\\\}.$ We study the mixed problem (1) from the point of view of control theory, taking the initial data $\\\\bar u$ fixed, and regarding the boundary data $\\\\widetilde u_a, \\\\widetilde u_b$ as control functions that vary in prescribed sets $\\\\U_a, \\\\U_b$, of $\\\\li$ boundary controls. In particular, we consider the family of configurations $$ \\\\A(T) \\\\doteq \\\\big\\\\{u(T,\\\\cdot); ~ u {\\\\rm is a sol. to} (1), \\\\quad \\\\widetilde u_a\\\\in \\\\U_a, \\\\widetilde u_b \\\\in \\\\U_b \\\\big\\\\} $$ 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 $lu$ topology.},
doi = {10.1137/S0363012902407776},
url = {http://hdl.handle.net/1963/1581},
author = {Fabio Ancona and Giuseppe Maria Coclite}
}