Some Results on the Boundary Control of Systems of Conservation Laws

Fabio Ancona (), Alberto Bressan () and Giuseppe Maria Coclite ()
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Fabio Ancona: P.zza Porta S. Donato, Dipartimento di Matematica and C.I.R.A.M.
Alberto Bressan: SISSA-ISAS
Giuseppe Maria Coclite: SISSA-ISAS

A chapter in Hyperbolic Problems: Theory, Numerics, Applications, 2003, pp 255-264 from Springer

Abstract: Abstract Consider an n × n system of conservation laws on a bounded interval (1) $$ {{u}_{t}} + f{{(u)}_{x}} = 0\quad t \geqslant 0,\;x \in ]a,b[, $$ with the intial condition (2) $$ u(0,x) = \varphi (x),\quad a \leqslant x \leqslant b, $$ and a weak form of the Dirichlet boundary conditions (3) $$ {{u}_{i}}(t,a) = {{\alpha }_{i}}(t),\quad {{u}_{i}}(t,b) = {{\beta }_{i}}(t),\quad t > 0 $$ (see [13, 14, 19] and reference therein for several weak formulations (3)).

Keywords: Weak Solution; Hyperbolic System; Rarefaction Wave; Constant State; Boundary Control (search for similar items in EconPapers)
Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-55711-8_22

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DOI: 10.1007/978-3-642-55711-8_22

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