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Adimurthi; Ghoshal, Shyam Sundar; Gowda, G. D. Veerappa

Exact controllability of scalar conservation laws with strict convex flux. (English) Zbl 1310.35232

Math. Control Relat. Fields 4, No. 4, 401-449 (2014).
Summary: We consider the scalar conservation law with strict convex flux in one space dimension. In this paper we study the exact controllability of entropy solution by using initial or boundary data control. Some partial results have been obtained in [F. Ancona and A. Marson, SIAM J. Control Optim. 36, No. 1, 290–312 (1998; Zbl 0919.35082); T. Horsin, ESAIM, Control Optim. Calc. Var. 3, 83–95 (1998; Zbl 0897.93034)]. Here we investigate the precise conditions under which, the exact controllability problem admits a solution. The basic ingredients in the proof of these results are, Lax-Oleinik [L. C. Evans, Partial differential equations. Providence, RI: American Mathematical Society (1998; Zbl 0902.35002)] explicit formula and finer properties of the characteristics curves.

Cited in 24 Documents

MSC:

35Q93 PDEs in connection with control and optimization
35L65 Hyperbolic conservation laws

Keywords:

Hamilton-Jacobi equation; scalar conservation laws; characteristics; controllability

Citations:

Zbl 0919.35082; Zbl 0897.93034; Zbl 0902.35002
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\textit{Adimurthi} et al., Math. Control Relat. Fields 4, No. 4, 401--449 (2014; Zbl 1310.35232)
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