Distributed control of the generalized Korteweg-de Vries-Burgers equation.
Divergence stability in connection with the -version of the finite element method
Domain decomposition methods for solving the Burgers equation
This article presents some results of numerical tests of solving the two-dimensional non-linear unsteady viscous Burgers equation. We have compared the known convergence and parallel performance properties of the additive Schwarz domain decomposition method with or without a coarse grid for the model Poisson problem with those obtained by experiments for the Burgers problem.
Domain Decomposition Schemes for the Stokes Equation
Domain Embedding Methods for the Stokes Equations.
Double bubbles minimize.
Doubly asymptotic trajectories of Lagrangian systems and a problem by Kirchhoff
We consider Lagrangian systems with Lagrange functions which exhibit a quadratic time dependence. We prove the existence of infinitely many solutions tending, as , to an «equilibrium at infinity». This result is applied to the Kirchhoff problem of a heavy rigid body moving through a boundless incompressible ideal fluid, which is at rest at infinity and has zero vorticity.
Dual combined finite element methods for non-newtonian flow (II). Parameter-dependent problem
Dual Combined Finite Element Methods For Non-Newtonian Flow (II) Parameter-Dependent Problem
This is the second part of the paper for a Non-Newtonian flow. Dual combined Finite Element Methods are used to investigate the little parameter-dependent problem arising in a nonliner three field version of the Stokes system for incompressible fluids, where the viscosity obeys a general law including the Carreau's law and the Power law. Certain parameter-independent error bounds are obtained which solved the problem proposed by Baranger in [4] in a unifying way. We also give some stable finite...
Dual integral equations -- revisited.
Dual variable methods for mixed-hybrid finite element approximation of the potential fluid flow problem in porous media.
Dual-mixed finite element methods for the Navier-Stokes equations
A mixed finite element method for the Navier–Stokes equations is introduced in which the stress is a primary variable. The variational formulation retains the mathematical structure of the Navier–Stokes equations and the classical theory extends naturally to this setting. Finite element spaces satisfying the associated inf–sup conditions are developed.
Dynamic pressure in relativistic thermodynamics
Dynamic programming for the stochastic Navier-Stokes equations
Dynamic Programming for the stochastic Navier-Stokes equations
We solve an optimal cost problem for a stochastic Navier-Stokes equation in space dimension 2 by proving existence and uniqueness of a smooth solution of the corresponding Hamilton-Jacobi-Bellman equation.
Dynamics of a Reactive Thin Film
Consider the dynamics of a thin film flowing down an inclined plane under the action of gravity and in the presence of a first-order exothermic chemical reaction. The heat released by the reaction induces a thermocapillary Marangoni instability on the film surface while the film evolution affects the reaction by influencing heat/mass transport through convection. The main parameter characterizing the reaction-diffusion process is the Damköhler number. We investigate the complete range of Damköhler...
Dynamics of Biomembranes: Effect of the Bulk Fluid
We derive a biomembrane model consisting of a fluid enclosed by a lipid membrane. The membrane is characterized by its Canham-Helfrich energy (Willmore energy with area constraint) and acts as a boundary force on the Navier-Stokes system modeling an incompressible fluid. We give a concise description of the model and of the associated numerical scheme. We provide numerical simulations with emphasis on the comparisons between different types of flow:...
Dynamics of granular fluids
Dynamics of Singularity Surfaces for Compressible Navier-Stokes Flows in Two Space Dimensions
We prove the global existence of solutions of the Navier-Stokes equations of compressible, barotropic flow in two space dimensions with piecewise smooth initial data. These solutions remain piecewise smooth for all time, retaining simple jump discontinuities in the density and in the divergence of the velocity across a smooth curve, which is convected with the flow. The strengths of these discontinuities are shown to decay exponentially in time, more rapidly for larger acoustic speeds and smaller...
Ecological modeling and Lagrangian approach
A mathematical model is proposed for a quantitative estimation of the damage to biological resources resulting from a pollutant discharge into an aqueous environment. On the basis of the Lagrangian description of fluid motion a set of hydrophysical parameters is introduced with help of which hydrobiologists can estimate the damage. The computation of parameters introduced is illustrated by the example of a model problem of a pollutant spreading in a canal. For the discretization of the problem a...