The compressible Navier–Stokes–Cahn–Hilliard equations with dynamic boundary conditions

2019 ◽  
Vol 29 (14) ◽  
pp. 2557-2584 ◽  
Author(s):  
Laurence Cherfils ◽  
Eduard Feireisl ◽  
Martin Michálek ◽  
Alain Miranville ◽  
Madalina Petcu ◽  
...  
Keyword(s):  
Initial Data ◽  
Binary Mixture ◽  
Boundary Conditions ◽  
Finite Energy ◽  
Immiscible Fluids ◽  
Navier Stokes ◽  
Physical Domain ◽  
Dynamic Boundary Conditions ◽  
Dynamic Boundary ◽  
Rigid Walls

We consider the compressible Navier–Stokes–Cahn–Hilliard system describing the behavior of a binary mixture of compressible, viscous and macroscopically immiscible fluids. The equations are endowed with dynamic boundary conditions which allows taking into account the interaction between the fluid components and the rigid walls of the physical domain. We establish the existence of global-in-time weak solutions for any finite energy initial data.

Solutions in Lebesgue spaces of the Navier-Stokes equations with dynamic boundary conditions

1993 ◽  
Vol 123 (4) ◽  
pp. 745-761 ◽  
Author(s):  
Marié Grobbelaar-Van Dalsen ◽  
Niko Sauer
Keyword(s):  
Boundary Conditions ◽  
Stokes Equations ◽  
Stokes Problem ◽  
Navier Stokes ◽  
Regularity Conditions ◽  
Dynamic Boundary Conditions ◽  
Lebesgue Spaces ◽  
Navier Stokes Equations ◽  
Dynamic Boundary ◽  
Initial States

SynopsisThis paper, although self-contained, is a continuation of the work done in [8], where the motion of a viscous, incompressible fluid is considered in conjunction with the rotation of a rigid body which is immersed in the fluid. The resulting mathematical model is a Navier-Stokes problem with dynamic boundary conditions. In [8] a uniqueL2,3solution is constructed under certain regularity assumptions on the initial states. In this paper we consider the Navier-Stokes problem with dynamic boundary conditions in the Lebesgue spacesLr,3(3<r<∞) and prove the existence of a unique solution, local in time, without imposing any regularity conditions on the initial states.

The coupled Cahn–Hilliard/Allen–Cahn system with dynamic boundary conditions

2021 ◽  
pp. 1-27
Author(s):  
Ahmad Makki ◽  
Alain Miranville ◽  
Madalina Petcu
Keyword(s):  
Fractal Dimension ◽  
Boundary Conditions ◽  
Well Posedness ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Dynamic Boundary Conditions ◽  
Finite Dimensional ◽  
Dynamic Boundary ◽  
Long Time ◽  
Finite Fractal Dimension

In this article, we are interested in the study of the well-posedness as well as of the long time behavior, in terms of finite-dimensional attractors, of a coupled Allen–Cahn/Cahn–Hilliard system associated with dynamic boundary conditions. In particular, we prove the existence of the global attractor with finite fractal dimension.

scholarly journals An inverse problem of radiative potentials and initial temperatures in parabolic equations with dynamic boundary conditions

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
El Mustapha Ait Ben Hassi ◽  
Salah-Eddine Chorfi ◽  
Lahcen Maniar
Keyword(s):  
Inverse Problem ◽  
Boundary Conditions ◽  
Parabolic Equations ◽  
Stability Result ◽  
Stability Estimate ◽  
Lipschitz Stability ◽  
Dynamic Boundary Conditions ◽  
Logarithmic Convexity ◽  
Dynamic Boundary ◽  
Logarithmic Stability

Abstract We study an inverse problem involving the restoration of two radiative potentials, not necessarily smooth, simultaneously with initial temperatures in parabolic equations with dynamic boundary conditions. We prove a Lipschitz stability estimate for the relevant potentials using a recent Carleman estimate, and a logarithmic stability result for the initial temperatures by a logarithmic convexity method, based on observations in an arbitrary subdomain.

Updating Substructure Models With Dynamic Boundary Conditions

1995 ◽  
Author(s):  
Michael Link ◽  
Zheng Qian
Keyword(s):  
Boundary Conditions ◽  
Dynamic Stiffness ◽  
Design Parameters ◽  
Physical Parameters ◽  
Model Parameters ◽  
Dynamic Boundary Conditions ◽  
Main Structure ◽  
Modal Data ◽  
Residual Structure ◽  
Dynamic Boundary

Abstract In recent years procedures for updating analytical model parameters have been developed by minimizing differences between analytical and preferably experimental modal analysis results. Provided that the initial analysis model contains parameters capable of describing possible damage these techniques could also be used for damage detection. In this case the parameters are updated using test data before and after the damage. Looking at complex structures with hundreds of parameters one generally has to measure the modal data at many locations and try to reduce the number of unknown parameters by some kind of localization technique because the measurement information is generally not sufficient to identify all the parameters equally distributed all over the structure. Another way of reducing the number of parameters shall be presented here. This method is based on the idea of measuring only a part of the structure and replacing the residual structure by dynamic boundary conditions which describe the dynamic stiffness at the interfaces between the measured main structure and the remaining unmeasured residual structure. This approach has some advantage since testing could be concentrated on critical areas where structural modifications are expected either due to damage or due to intended design changes. The dynamic boundary conditions are expressed in Craig-Bampton (CB) format by transforming the mass and stiffness matrices of the unmeasured residual structure to the interface degrees of freedom (DOF) and to the modal DOFs of the residual structure fixed at the interface. The dynamic boundary stiffness concentrates all physical parameters of the residual structure in only a few parameters which are open for updating. In this approach damage or modelling errors within the unmeasured residual structure are taken into account only in a global sense whereas the measured main structure is parametrized locally as usual by factoring mass and stiffness submatrices defining the type and the location of the physical parameters to be identified. The procedure was applied to identify the design parameters of a beam type frame structure with bolted joints using experimental modal data.

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