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- W2041931018 abstract "We consider the initial value problem with boundary control for a scalar nonlinear conservation law begin{equation*} u_t+[f(u)]_x=0,qquadqquad u(0,x)=0,qquad u(cdot,0)= tilde uin{cal U},tag{$ast$} end{equation*} on the domain $Omega={(t,x)inreal^2: tgeq 0, xgeq 0}$. Here $u=u(t,x)$ is the state variable, ${cal U}$ is a set of bounded boundary data regarded as controls, and f is assumed to be strictly convex. We give a characterization of the set of attainable profiles at a fixed time $T>0$ and at a fixed point $bar x>0$: begin{equation*} begin{aligned} rag &={u(T,cdot): u hbox{is a solution of} (ast)}, ragx &={u(cdot,bar x): u hbox{is a solution of} (ast)}, end{aligned} qquadquad{cal U}= ellein({Bbb R}^+). end{equation*} Moreover we prove that $rag$ and $ragx$ are compact subsets of $elleuno$ and $elleuno_{loc}$, respectively, whenever ${cal U}$ is a set of controls which pointwise satisfy closed convex constraints, together with some additional integral inequalities." @default.
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- W2041931018 date "1998-01-01" @default.
- W2041931018 modified "2023-10-17" @default.
- W2041931018 title "On the Attainable Set for Scalar Nonlinear Conservation Laws with Boundary Control" @default.
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- W2041931018 doi "https://doi.org/10.1137/s0363012996304407" @default.
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