tailieunhanh - On uniqueness of a classical solution of the system of non-linear 1-D saint venant equations

In this paper the theorem of uniqueness of a classical solution of the system of non-linear 1-D Saint Venant equations is proved. This uniqueness theorem is setup for the system of non-linear 1-D Saint Venant equations in canonical form under respective initial and boqndary condiiions. | Vietnam Journal of Mechanics, NCST of Vietnam Vol. ~1, 1999, No 4 {231 - 238) ON UNIQUENESS OF A CLASSICAL SOLUTION OF THE SYSTEM OF NON-LINEAR 1-D SAINT VENANT EQUATIONS HOANG VAN LAI Institute of Information Technology LE MAU LONG Branch of Institute of Information Technology in HoChiMinh City MAl DINH TRUNG Institute of Mechanics ABSTRACT. In this paper the theorem of uniqueness of a classical solution of the system of non-linear 1-D Saint Venant equations is proved. This uniqueness theorem is setup for the system of non-linear 1-D Saint Venant equations in canonical form under respective initial and boqndary condiiions. 1. Introduction The system of 1-D Saint Venant equations describes flows in a river or open channel. It became kernel of a mathematical modeling for the river flow simulat ion. Problem of uniqueness of a classical solution of this system of equations is important especially in the non-linear case. 2. Boundary Condition for the System of 1-D Saint Venant Equations · . System of 1-D Saint Venant Equations The System of 1-D Saint Venant Equations [1] describes a flow in river or open channel system. There are several forms of this system (see [2]). In this paper, we use the system of 1-D Saint Venant equations in the following form: ah ah Aau -·&t +u-+ ax -b -ax =0 . au ah au . -at + g -ax + u -ax = -g(St- So) where: with 0 :::; x :::; L and 0 :::; t :::; T h - Depth of water in the river /channel 231 () u- Velocity of the river/channel flow A - Cross section area of the riverJchannel flow b - Width of water in the river/ channel S 1 - Force due to bottom friction Sa- Force due to gravity The system of equations () is d~vised from the system of equations () in [2] assuming that cr~ss section 0). Achanges slowly alo~g X (thus ( aaA) h=const ~ X . Canonical Form of the System of 1-D Saint Venant Equations The system (2:1) is a system of first order partial differential equations. In order to analyze .