Interfacial dynamics for thermodynamically consistent phase-field models with nonconserved order parameter.
Fife, Paul C., Penrose, Oliver (1995)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Fife, Paul C., Penrose, Oliver (1995)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Nelson, M.I. (2000)
Journal of Applied Mathematics and Decision Sciences
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William B. Dunbar, Nicolas Petit, Pierre Rouchon, Philippe Martin (2003)
ESAIM: Control, Optimisation and Calculus of Variations
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In this paper we consider a free boundary problem for a nonlinear parabolic partial differential equation. In particular, we are concerned with the inverse problem, which means we know the behavior of the free boundary a priori and would like a solution, e.g. a convergent series, in order to determine what the trajectories of the system should be for steady-state to steady-state boundary control. In this paper we combine two issues: the free boundary (Stefan) problem with a quadratic...
Knežević-Miljanović, J. (1996)
Matematichki Vesnik
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Branko J. Malešević (1999)
Matematički Vesnik
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Dawson, Donald A., Greven, Andreas (1999)
Electronic Journal of Probability [electronic only]
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Ilya Kostin, Martine Marion, Rozenn Texier-Picard, Vitaly A. Volpert (2003)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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When two miscible fluids, such as glycerol (glycerin) and water, are brought in contact, they immediately diffuse in each other. However if the diffusion is sufficiently slow, large concentration gradients exist during some time. They can lead to the appearance of an “effective interfacial tension”. To study these phenomena we use the mathematical model consisting of the diffusion equation with convective terms and of the Navier-Stokes equations with the Korteweg stress. We prove the...
Kolokol'tsov, Vassili N. (2001)
Electronic Journal of Probability [electronic only]
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James M. Greenberg (2001)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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In this paper we focus on melting and solidification processes described by phase-field models and obtain rigorous estimates for such processes. These estimates are derived in Section 2 and guarantee the convergence of solutions to non-constant equilibrium patterns. The most basic results conclude with the inequality (E2.31). The estimates in the remainder of Section 2 illustrate what obtains if the initial data is progressively more regular and may be omitted on first reading. We also...
Finley, J. D. III (2000)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Jerry L. Kazdan (2001)
The Teaching of Mathematics
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