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Within the context of the inverse Lie problem the question whether there exist PDEs that are characterized by their Lie point symmetries may be addressed. In a recent paper the authors called these equations Lie remarkable. In this paper we exhibit various examples of Lie remarkable equations, including some multidimensional Monge-Ampere type equations.
G. MANNO, OLIVERI, Francesco, R. VITOLO
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Extremum seeking boundary control for PDE–PDE cascades
Systems & Control Letters, 2021The manuscript addresses the problem of extremum seeking for wave equations evolving in the one-dimensional spatial interval~\((0,1)\subset\mathbb R\). \par The input control acts on the right spatial boundary point~\(x=1\); see Eqs.~(4)--(7). The authors also consider the case where such input is subject to the solution of a heat equation; see Eqs ...
Oliveira, Tiago Roux, Krstic, Miroslav
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