Abstract:We present a transient mathematical model for the sublimation growth of silicon carbide (SiC) single crystals by the physical vapor transport (PVT) method. The model of the gas phase consists of balance equations for mass, momentum, and energy, as well as reaction-diffusion equations. Due to physical and chemical reactions, the gas phase is encompassed by free boundaries. Nonlinear heat transport equations are considered in the various solid components of the growth system. Discontinuous and nonlocal interface… Show more
“…Due to the high temperatures and the low pressure, the powder sublimates and crystallizes at a single-crystalline seed located at the cooled top of the cavity, such that the desired single crystal grows into the reaction chamber. See [6] for more details.…”
Abstract. We consider a control constrained optimal control problem governed by a semilinear elliptic equation with nonlocal interface conditions. These conditions occur during the modeling of diffusegray conductive-radiative heat transfer. After stating first-order necessary conditions, second-order sufficient conditions are derived that account for strongly active sets. These conditions ensure local optimality in an L s -neighborhood of a reference function whereby the underlying analysis allows to use weaker norms than L ∞ .Mathematics Subject Classification. 49K20, 35J65, 80M50.
“…Due to the high temperatures and the low pressure, the powder sublimates and crystallizes at a single-crystalline seed located at the cooled top of the cavity, such that the desired single crystal grows into the reaction chamber. See [6] for more details.…”
Abstract. We consider a control constrained optimal control problem governed by a semilinear elliptic equation with nonlocal interface conditions. These conditions occur during the modeling of diffusegray conductive-radiative heat transfer. After stating first-order necessary conditions, second-order sufficient conditions are derived that account for strongly active sets. These conditions ensure local optimality in an L s -neighborhood of a reference function whereby the underlying analysis allows to use weaker norms than L ∞ .Mathematics Subject Classification. 49K20, 35J65, 80M50.
“…At the boundary of the transparent cavity Σ, the conductive heat flux has a discontinuity (14) equal to the difference between the heat radiation outgoing from the surface, denoted by R, and the heat radiation incoming at the surface, denoted by J. We follow the approach of [11], standard in crystal growth, to model the quantities R and J. The main assumption is that all the opaque materials involved are diffuse grey, so that their emission properties do not depend on the wavelength of the radiation.…”
Section: Introductionmentioning
confidence: 99%
“…We will address the problem of finding fields v, H, B, E, D, j and scalars p, θ that satisfy (2), (3), (12), (13), (5), (17), (23), (6), (7), (8), (9), (10), (11), (18), and (19), as Problem (P ).…”
Section: Introductionmentioning
confidence: 99%
“…The requirement (10) is a consequence of charge conservation in the absence of free charges. Finally, (11) are the constitutive relations characterizing linear media. The use of this type of model for the electromagnetic part of the problem is justified in the reference [1].…”
“…Models of radiative heat transfer have recently been studied from the point of view of applied mathematics in different publications: e.g. [16], [5], [4] for modeling and numerics, [11] for control theory, [7] for analysis.…”
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.