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Solutions of a nonhyperbolic pair of balance laws

Michael Sever (2005)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We describe a constructive algorithm for obtaining smooth solutions of a nonlinear, nonhyperbolic pair of balance laws modeling incompressible two-phase flow in one space dimension and time. Solutions are found as stationary solutions of a related hyperbolic system, based on the introduction of an artificial time variable. As may be expected for such nonhyperbolic systems, in general the solutions obtained do not satisfy both components of the given initial data. This deficiency may be overcome,...

Solutions of a nonhyperbolic pair of balance laws

Michael Sever (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We describe a constructive algorithm for obtaining smooth solutions of a nonlinear, nonhyperbolic pair of balance laws modeling incompressible two-phase flow in one space dimension and time. Solutions are found as stationary solutions of a related hyperbolic system, based on the introduction of an artificial time variable. As may be expected for such nonhyperbolic systems, in general the solutions obtained do not satisfy both components of the given initial data. This deficiency may be overcome,...

Solvability Conditions for a Linearized Cahn-Hilliard Equation of Sixth Order

V. Vougalter, V. Volpert (2012)

Mathematical Modelling of Natural Phenomena

We obtain solvability conditions in H6(ℝ3) for a sixth order partial differential equation which is the linearized Cahn-Hilliard problem using the results derived for a Schrödinger type operator without Fredholm property in our preceding article [18].

Solvability of the stationary Stokes system in spaces H ² - μ , μ ∈ (0,1)

Ewa Zadrzyńska, Wojciech M. Zajączkowski (2010)

Applicationes Mathematicae

We consider the stationary Stokes system with slip boundary conditions in a bounded domain. Assuming that data functions belong to weighted Sobolev spaces with weights equal to some power of the distance to some distinguished axis, we prove the existence of solutions to the problem in appropriate weighted Sobolev spaces.

Some remarks on Prandtl system

Hua Shui Zhan, Jun Ning Zhao (2008)

Applications of Mathematics

The purpose of this paper is to correct some drawbacks in the proof of the well-known Boundary Layer Theory in Oleinik’s book. The Prandtl system for a nonstationary layer arising in an axially symmetric incopressible flow past a solid body is analyzed.

Some Remarks on the Boundary Conditions in the Theory of Navier-Stokes Equations

Chérif Amrouche, Patrick Penel, Nour Seloula (2013)

Annales mathématiques Blaise Pascal

This article addresses some theoretical questions related to the choice of boundary conditions, which are essential for modelling and numerical computing in mathematical fluids mechanics. Unlike the standard choice of the well known non slip boundary conditions, we emphasize three selected sets of slip conditions, and particularly stress on the interaction between the appropriate functional setting and the status of these conditions.

Spatially-dependent and nonlinear fluid transport: coupling framework

Jürgen Geiser (2012)

Open Mathematics

We introduce a solver method for spatially dependent and nonlinear fluid transport. The motivation is from transport processes in porous media (e.g., waste disposal and chemical deposition processes). We analyze the coupled transport-reaction equation with mobile and immobile areas. The main idea is to apply transformation methods to spatial and nonlinear terms to obtain linear or nonlinear ordinary differential equations. Such differential equations can be simply solved with Laplace transformation...

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