Stability of a Resonant System of Conservation Laws Modeling Polymer Flow with Gravitation
نویسندگان
چکیده
We prove L 1 uniqueness and stability for a resonant 2 2 system of conservation laws that arise as a model for two phase polymer ow in porous media. The analysis uses the equivalence of the Eulerian and Lagrangian formulation of this system, and the results are rst established for an auxiliary scalar equation. Our methods are based on front tracking approximations for the auxiliary equation, and the Kru zkov entropy condition for scalar conservation laws. 1. Introduction We study the initial value problem for scalar conservation laws of type u t + f(a(x); u) x = 0; (1.1) where the coeecient a is a suitable function of x. Using the transformation given by Wagner in
منابع مشابه
Nonlinear Vibration and Instability Analysis of a PVDF Cylindrical Shell Reinforced with BNNTs Conveying Viscose Fluid Using HDQ Method
Using harmonic differential quadrature (HDQ) method, nonlinear vibrations and instability of a smart composite cylindrical shell made from piezoelectric polymer of polyvinylidene fluoride (PVDF) reinforced with boron nitride nanotubes (BNNTs) are investigated while clamped at both ends and subjected to combined electro-thermo-mechanical loads and conveying a viscous-fluid. The mathematical mode...
متن کاملVoltage Regulation of DC-DC Series Resonant Converter Operating in Discontinuous Conduction Mode: The Hybrid Control Approach
Dynamic modeling and control of dc-dc series resonant converter (SRC) especially when operating in discontinuous conduction mode (DCM) is still a challenge in power electronics. Due to semiconductors switching, SRC is naturally represented as a switched linear system, a class of hybrid systems. Nevertheless, the hybrid nature of the SRC is commonly neglected and it is modeled as a purely contin...
متن کاملGlobal Stabilization of Attitude Dynamics: SDRE-based Control Laws
The State-Dependant Riccati Equation method has been frequently used to design suboptimal controllers applied to nonlinear dynamic systems. Different methods for local stability analysis of SDRE controlled systems of order greater than two such as the attitude dynamics of a general rigid body have been extended in literature; however, it is still difficult to show global stability properties of...
متن کاملA Mass Conservative Method for Numerical Modeling of Axisymmetric flow
In this paper, the cell-centered finite volume method (CC-FVM) has been presented to simulate the axisymmetric radial flow toward a pumping well. The model is applied to the unstructured triangular grids which allows to simulate inhomogeneous and complex-shaped domains. Due to the non-orthogonality of the irregular grids, the multipoint flux approximation (MPFA) methods are used to discretize t...
متن کاملThe DFLU flux for systems of conservation laws
The DFLU numerical flux was introduced in order to solve hyperbolic scalar conservation laws with a flux function discontinuous in space. We show how this flux can be used to solve certain class of systems of conservation laws such as systems modeling polymer flooding in oil reservoir engineering. Furthermore, these results are extended to the case where the flux function is discontinuous in th...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1999