Well-posedness for an extended Penrose–Fife phase-field model with energy balance supplied by Dirichlet boundary conditions

2008 ◽  
Vol 9 (2) ◽  
pp. 370-383 ◽  
Author(s):  
Akio Ito ◽  
Masahiro Kubo
Keyword(s):  
Energy Balance ◽  
Boundary Conditions ◽  
Phase Field ◽  
Dirichlet Boundary ◽  
Field Model ◽  
Phase Field Model ◽  
Dirichlet Boundary Conditions ◽  
Well Posedness

The Penrose-Fife phase-field model with coupled dynamic boundary conditions

2014 ◽  
Vol 34 (10) ◽  
pp. 4259-4290 ◽  
Author(s):  
Alain Miranville ◽  
Elisabetta Rocca ◽  
Giulio Schimperna ◽  
Antonio Segatti
Keyword(s):  
Boundary Conditions ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Dynamic Boundary Conditions ◽  
Dynamic Boundary

scholarly journals GLOBAL AND EXPONENTIAL ATTRACTORS FOR THE PENROSE–FIFE SYSTEM

2009 ◽  
Vol 19 (06) ◽  
pp. 969-991 ◽  
Author(s):  
GIULIO SCHIMPERNA
Keyword(s):  
Phase Transitions ◽  
Energy Balance ◽  
Boundary Conditions ◽  
Balance Equation ◽  
Dirichlet Boundary ◽  
Energy Balance Equation ◽  
Dirichlet Boundary Conditions ◽  
Dynamical Process ◽  
Exponential Attractors

The Penrose–Fife system for phase transitions is addressed. Dirichlet boundary conditions for the temperature are assumed. Existence of global and exponential attractors is proved. Differently from preceding contributions, here the energy balance equation is both singular at 0 and degenerate at ∞. For this reason, the dissipativity of the associated dynamical process is not trivial and has to be proved rather carefully.

scholarly journals Existence and uniqueness of solution for Cahn-Hilliard hyperbolic phase field system with Dirichlet boundary conditions and polynomial potential

2018 ◽  
Vol 7 (1) ◽  
pp. 10
Author(s):  
A. J. Bissouesse ◽  
Daniel Moukoko ◽  
Franck Langa ◽  
Macaire Batchi
Keyword(s):  
Boundary Conditions ◽  
Phase Field ◽  
Dirichlet Boundary ◽  
Initial Conditions ◽  
Dirichlet Boundary Conditions ◽  
Uniqueness Of Solution ◽  
Polynomial Potential ◽  
Field System ◽  
Phase Field System ◽  
Homogeneous Dirichlet Boundary Conditions

Our aim in this article is to study the existence and the uniqueness of solution for Cahn-Hilliard hyperbolic phase-field system, with initial conditions, homogeneous Dirichlet boundary conditions, polynomial potential in a bounded and smooth domain.

scholarly journals Well Posedness for a Class of Flexible Structure in Hölder Spaces

2009 ◽  
Vol 2009 ◽  
pp. 1-13 ◽  
Author(s):  
Claudio Cuevas ◽  
Carlos Lizama
Keyword(s):  
Boundary Conditions ◽  
External Force ◽  
Dirichlet Boundary ◽  
Flexible Structures ◽  
Dirichlet Boundary Conditions ◽  
Flexible Structure ◽  
Well Posedness ◽  
Hölder Spaces ◽  
Holder Spaces ◽  
Well Posed

We characterize well-posedness in Hölder spaces for an abstract version of the equation(∗) u′′+λu′′′=c2(Δu+μΔu′)+fwhich model thevibrationsof flexible structures possessing internal material damping and external forcef. As a consequence, we show that in case of the Laplacian with Dirichlet boundary conditions, equation(∗)is always well-posed provided0<λ<μ.

scholarly journals On the cubic NLS on 3D compact domains

2013 ◽  
Vol 13 (1) ◽  
pp. 1-18 ◽  
Author(s):  
Fabrice Planchon
Keyword(s):  
Schrödinger Equation ◽  
Boundary Conditions ◽  
Bounded Domain ◽  
Schrodinger Equation ◽  
Dirichlet Boundary ◽  
Smooth Boundary ◽  
Dirichlet Boundary Conditions ◽  
Well Posedness ◽  
Bounded Domains ◽  
Bilinear Estimates

AbstractWe prove bilinear estimates for the Schrödinger equation on 3D domains, with Dirichlet boundary conditions. On non-trapping domains, they match the ${ \mathbb{R} }^{3} $ case, while on bounded domains they match the generic boundaryless manifold case. We obtain, as an application, global well-posedness for the defocusing cubic NLS for data in ${ H}_{0}^{s} (\Omega )$, $1\lt s\leq 3$, with $\Omega $ any bounded domain with smooth boundary.

Anisotropic Li intercalation in a LixFePO4 nano-particle: a spectral smoothed boundary phase-field model

2016 ◽  
Vol 18 (14) ◽  
pp. 9537-9543 ◽  
Author(s):  
L. Hong ◽  
L. Liang ◽  
S. Bhattacharyya ◽  
W. Xing ◽  
L. Q. Chen
Keyword(s):  
Phase Transformation ◽  
Boundary Conditions ◽  
Phase Field ◽  
Composite Electrode ◽  
Field Model ◽  
Phase Field Model ◽  
Boundary Phase ◽  
Nano Particle

Spectral smoothed boundary phase-field model for studying phase transformation and implementing boundary conditions in a heterogeneous composite electrode.

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