Differential and Integral Equations

On some linearized problems of shallow water flows

Tran Thu u Ha, C. Licht, and Quoc Phong Vu

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There are many papers devoted to the study of shallow water flows especially by numerical methods. In this note, we give a mathematical analysis, based on the theory of semigroups of operators on Hilbert space, of two linearized problems involving the Saint-Venant equations governing shallow water flows. The first one concerns the classical linearized Saint-Venant problem, while the second one deals with the water quality problem: the evolution of a concentration of products in a flow solution of the first problem.

Article information

Differential Integral Equations, Volume 22, Number 3/4 (2009), 275-283.

First available in Project Euclid: 20 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47F05: Partial differential operators [See also 35Pxx, 58Jxx] (should also be assigned at least one other classification number in section 47) 47D06: One-parameter semigroups and linear evolution equations [See also 34G10, 34K30] 35Q35: PDEs in connection with fluid mechanics 74G50: Saint-Venant's principle


Licht, C.; Ha, Tran Thu u; Vu, Quoc Phong. On some linearized problems of shallow water flows. Differential Integral Equations 22 (2009), no. 3/4, 275--283. https://projecteuclid.org/euclid.die/1356019774

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