scholarly journals Well-posedness and approximation of a measure-valued mass evolution problem with flux boundary conditions

2014 ◽  
Vol 352 (1) ◽  
pp. 51-54 ◽  
Author(s):  
Joep Evers ◽  
Sander C. Hille ◽  
Adrian Muntean
Keyword(s):  
Boundary Conditions ◽  
Evolution Problem ◽  
Well Posedness ◽  
Flux Boundary Conditions

scholarly journals Local Well-Posedness for Free Boundary Problem of Viscous Incompressible Magnetohydrodynamics

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 461
Author(s):  
Kenta Oishi ◽  
Yoshihiro Shibata
Keyword(s):  
Free Surface ◽  
Free Boundary ◽  
Boundary Conditions ◽  
Stokes Equations ◽  
Mhd Flow ◽  
Transmission Conditions ◽  
Well Posedness ◽  
Anisotropic Space ◽  
Free Boundary Conditions ◽  
Incompressible Magnetohydrodynamics

In this paper, we consider the motion of incompressible magnetohydrodynamics (MHD) with resistivity in a domain bounded by a free surface. An electromagnetic field generated by some currents in an external domain keeps an MHD flow in a bounded domain. On the free surface, free boundary conditions for MHD flow and transmission conditions for electromagnetic fields are imposed. We proved the local well-posedness in the general setting of domains from a mathematical point of view. The solutions are obtained in an anisotropic space Hp1((0,T),Hq1)∩Lp((0,T),Hq3) for the velocity field and in an anisotropic space Hp1((0,T),Lq)∩Lp((0,T),Hq2) for the magnetic fields with 2<p<∞, N<q<∞ and 2/p+N/q<1. To prove our main result, we used the Lp-Lq maximal regularity theorem for the Stokes equations with free boundary conditions and for the magnetic field equations with transmission conditions, which have been obtained by Frolova and the second author.

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.

Inverse problem for a degenerate/singular parabolic system with Neumann boundary conditions

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Mohammed Alaoui ◽  
Abdelkarim Hajjaj ◽  
Lahcen Maniar ◽  
Jawad Salhi
Keyword(s):  
Boundary Conditions ◽  
Parabolic System ◽  
Source Term ◽  
Neumann Boundary ◽  
Stability Estimate ◽  
Carleman Estimates ◽  
Well Posedness ◽  
Degenerate Diffusion ◽  
Neumann Type ◽  
Lower Order Terms

AbstractIn this paper, we study an inverse source problem for a degenerate and singular parabolic system where the boundary conditions are of Neumann type. We consider a problem with degenerate diffusion coefficients and singular lower-order terms, both vanishing at an interior point of the space domain. In particular, we address the question of well-posedness of the problem, and then we prove a stability estimate of Lipschitz type in determining the source term by data of only one component. Our method is based on Carleman estimates, cut-off procedures and a reflection technique.

Boundary conditions for Maxwell fields in Kerr-AdS spacetimes

2016 ◽  
Vol 25 (09) ◽  
pp. 1641011 ◽  
Author(s):  
Mengjie Wang
Keyword(s):  
Black Holes ◽  
Angular Momentum ◽  
Boundary Conditions ◽  
Energy Flux ◽  
Momentum Flux ◽  
De Sitter ◽  
Perturbative Methods ◽  
Flux Boundary Conditions ◽  
Maxwell Fields ◽  
New Type

Perturbative methods are useful to study the interaction between black holes and test fields. The equation for a perturbation itself, however, is not complete to study such a composed system if we do not assign physically relevant boundary conditions. Recently we have proposed a new type of boundary conditions for Maxwell fields in Kerr-anti-de Sitter (Kerr-AdS) spacetimes, from the viewpoint that the AdS boundary may be regarded as a perfectly reflecting mirror, in the sense that energy flux vanishes asymptotically. In this paper, we prove explicitly that a vanishing energy flux leads to a vanishing angular momentum flux. Thus, these boundary conditions may be dubbed as vanishing flux boundary conditions.

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