Exact boundary observability of unsteady supercritical flows in a tree-like network of open canals

Qilong Gu

doi:10.1007/s11401-010-0595-2

Chinese Annals of Mathematics, Series B ›› 2010, Vol. 31 ›› Issue (4) : 447 -460. DOI: 10.1007/s11401-010-0595-2

Article

Exact boundary observability of unsteady supercritical flows in a tree-like network of open canals

Qilong Gu ¹^,²^,^a

Author information +

History +

PDF

Abstract

The author establishes the exact boundary observability of unsteady supercritical flows in a tree-like network of open canals with general topology. An implicit duality between the exact boundary controllability and the exact boundary observability is also given for unsteady supercritical flows.

Keywords

Exact boundary observability / Saint-Venant system / Tree-like network of open canals / Quasilinear hyperbolic system

Cite this article

Download citation ▾

Qilong Gu. Exact boundary observability of unsteady supercritical flows in a tree-like network of open canals. Chinese Annals of Mathematics, Series B, 2010, 31(4): 447-460 DOI:10.1007/s11401-010-0595-2

登录浏览全文

4963

注册一个新账户忘记密码

References

Publishing order | Descend order by publishing year | Descend order by cited within

[1]	Gu Q. L.. Exact boundary controllability of unsteady supercritical flows in a tree-like network of open canals. Math. Meth. Appl. Sci., 2008, 31: 1497-1508

[2]	Gu Q. L., Li T. T.. Exact boundary observability of unsteady flows in a tree-like network of open canals. Math. Meth. Appl. Sci., 2009, 32: 395-418

[3]	Gugat M., Leugering G., Schmidt E. G.. Global controllability between steady supercritical flows in channel networks. Math. Meth. Appl. Sci., 2004, 27: 781-802

[4]	Leugering G., Schmidt E. G.. On the modelling and stabilization of flows in networks of open canals. SIAM J. Control Optim., 2002, 41: 164-180

[5]	Li T. T.. Exact boundary controllability for quasilinear hyperbolic systems and its application to unsteady flows in a network of open canals. Math. Meth. Appl. Sci., 2004, 27: 1089-1114

[6]	Li T. T.. Exact boundary controllability of unsteady flows in a network of open canals. Math. Nachr., 2005, 278: 278-289

[7]	Li T. T.. Observabilité exacte frontière pour des systèmes hyperboliques quasi linéaires. C. R. Acad. Sci. Paris, Ser. I, 2006, 342: 937-942

[8]	Li T. T.. Exact boundary observability for quasilinear hyperbolic systems. ESIAM: Control, Optimisation and Calculus of Variations, 2008, 14: 759-766

[9]	Li T. T., Jin Y.. Semi-global C ¹ solution to the mixed initial-boundary value problem for quasilinear hyperbolic systems. Chin. Ann. Math., 2001, 22B(3): 325-336

[10]	Li T. T., Rao B. P.. Exact boundary controllability for quasilinear hyperbolic systems. SIAM J. Control Optim., 2003, 41: 1748-1755

[11]	Li T. T., Rao B. P.. Local exact boundary controllability for a class of quasilinear hyperbolic systems. Chin. Ann. Math., 2002, 23B(2): 209-218

[12]	Li T. T., Rao B. P.. Contrôlabilité exacte frontière de l’écoulement d’un fluide non-stationnaire dans un réseau du type d’arbre de canaux ouverts. C. R. Acad. Sci. Paris, Ser. I, 2004, 339: 867-872

[13]	Li T. T., Rao B. P.. Exact boundary controllability of unsteady flows in a tree-like network of open canals. Meth. Appl. Anal., 2004, 11: 353-366

[14]	de Saint-Venant B.. Théorie du mouvement non permanent des eaux, avec application aux crues des rivières et l’introduction des marées dans leur lit. C. R. Acad. Sci., 1871, 73: 147-154