Interdiffusion and Stress, Free Boundary Problem for r - Component (r > 2) One Dimensional Mixture Showing Constant Concentration

1996 ◽  
Vol 129-130 ◽  
pp. 295-296
Author(s):  
Marek Danielewski ◽  
K. Holly ◽  
B. Bozek ◽  
Robert Filipek
Keyword(s):  
Free Boundary ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Constant Concentration ◽  
One Dimensional ◽  
Stress Free Boundary

scholarly journals On the Solution of a Hyperbolic One-Dimensional Free Boundary Problem for a Maxwell Fluid

2011 ◽  
Vol 2011 ◽  
pp. 1-26
Author(s):  
Lorenzo Fusi ◽  
Angiolo Farina
Keyword(s):  
Free Boundary ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Boundary Data ◽  
Inner Core ◽  
Representation Formula ◽  
Maxwell Fluid ◽  
Explicit Representation ◽  
Boundary Equation ◽  
One Dimensional

We study a hyperbolic (telegrapher's equation) free boundary problem describing the pressure-driven channel flow of a Bingham-type fluid whose constitutive model was derived in the work of Fusi and Farina (2011). The free boundary is the surface that separates the inner core (where the velocity is uniform) from the external layer where the fluid behaves as an upper convected Maxwell fluid. We present a procedure to obtain an explicit representation formula for the solution. We then exploit such a representation to write the free boundary equation in terms of the initial and boundary data only. We also perform an asymptotic expansion in terms of a parameter tied to the rheological properties of the Maxwell fluid. Explicit formulas of the solutions for the various order of approximation are provided.

A free boundary problem arising in the modelling of internal oxidation of binary alloys

1995 ◽  
Vol 6 (3) ◽  
pp. 225-245
Author(s):  
Bei Hu ◽  
Jianhua Zhang
Keyword(s):  
Free Boundary ◽  
Boundary Problem ◽  
Internal Oxidation ◽  
Free Boundary Problem ◽  
Binary Alloys ◽  
Local Existence ◽  
Discontinuous Coefficients ◽  
Parabolic Partial Differential Equation ◽  
One Dimensional ◽  
A Free Boundary Problem

A one-dimensional free boundary problem arising in the modelling of internal oxidation of binary alloys is studied in this paper. The free boundary of this problem is determined by the equation u = 0, where u is the solution of a parabolic partial differential equation with discontinuous coefficients across the free boundary. Local existence, uniqueness and the regularity of the free boundary are established. Global existence is also studied.

FROM THE IMPLIED VOLATILITY SKEW TO A ROBUST CORRECTION TO BLACK-SCHOLES AMERICAN OPTION PRICES

2001 ◽  
Vol 04 (04) ◽  
pp. 651-675 ◽  
Author(s):  
JEAN-PIERRE FOUQUE ◽  
GEORGE PAPANICOLAOU ◽  
K. RONNIE SIRCAR
Keyword(s):  
Free Boundary ◽  
Boundary Problem ◽  
Stochastic Volatility ◽  
Free Boundary Problem ◽  
Implied Volatility ◽  
Stochastic Volatility Model ◽  
Option Prices ◽  
One Dimensional ◽  
Volatility Model ◽  
Black Scholes

We describe a robust correction to Black-Scholes American derivatives prices that accounts for uncertain and changing market volatility. It exploits the tendency of volatility to cluster, or fast mean-reversion, and is simply calibrated from the observed implied volatility skew. The two-dimensional free-boundary problem for the derivative pricing function under a stochastic volatility model is reduced to a one-dimensional free-boundary problem (the Black-Scholes price) plus the solution of a fixed boundary-value problem. The formal asymptotic calculation that achieves this is presented here. We discuss numerical implementation and analyze the effect of the volatility skew.

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