We present a bibliography on moving and free boundary problems for the heatdiffusion equation, particularly regarding the Stefan and related problems. It contains 5869 titles referring to 588 scientific Journals, 122 books, 88 symposia (having at least 3 contributions on the subject), 30 collections, 59 thesis and 247 technical reports. It tries to give a comprehensive account of the western existing mathematicalphysical-engineering literature on this research field. RESUMEN Se presenta una bibliografía sobre problemas de frontera móvil y libre para la ecuación del calor-difusión, en particular sobre el problema de Stefan y problemas relacionados. Contiene 5869 títulos distribuidos en 588 revistas científicas, 122 libros, 88 simposios (teniendo al menos 3 contribuciones en el tema), 30 colecciones, 59 tesis y 247 informes técnicos o prepublicaciones. Se da un informe amplio de la bibliografía matemática, física y de las ingenierías existente en occidente sobre este tema de investigación. Primary Mathematics Subject Classification Number (*): 35R35, 80A22 Secondary Mathematics Subject Classification Number (*): 35B40, 35C05, 35C15, 35Kxx, 35R30, 46N20, 49J20, 65Mxx, 65Nxx, 76R50, 76S05, 76T05, 93C20. (*) Following the 1991 Mathematics Subject Classification compiled by Mathematical Reviews and Zentralblatt fur Mathematik. Primary key words: Enthalpy formulation or method, Filtration, Free boundary problems, Freezing, Melting, Moving boundary problems, Mushy region, Phase-change problem, Solidification, Stefan problem. Secondary key words: Continuous mechanics, Diffusion process, Functional analysis, Heat conduction, Mathematical methods, Numerical methods, Partial differential equations, Variational inequalities, Weak solutions. Palabras claves primarias: Método o formulación en entalpía, Filtración, Problemas de frontera libre, Congelación, Derretimiento, Problemas de frontera móvil, Región pastosa, Problema de cambio de fase, Solidificación, Problema de Stefan. Palabras claves secundarias: Mecánica del continuo, Procesos difusivos, Análisis funcional, Conducción del calor, Métodos matemáticos, Métodos numéricos, Ecuaciones diferenciales a derivadas parciales, Inecuaciones variacionales, Soluciones débiles. El manuscrito fue recibido y aceptado en octubre de 1999. D.A. Tarzia, A bibliography on FBP. The Stefan problem, MAT Serie A, # 2 (2000). 3

/pdf/a-bibliography-on-moving-free-boundary-problems-for-the-heat-zk5g33r15v.pdf

A bibliography on moving-free boundary problems for the heat-diffusion equation. The stefan and related problems

Carotenoid-to-chlorophyll energy transfer in recombinant major light-harvesting complex (LHCII) of higher plants. I. Femtosecond transient absorption measurements.

Exciton Dynamics in the Chlorosomal Antennae of the Green Bacteria Chloroflexus aurantiacus and Chlorobium tepidum

The CALGRID mesoscale photochemical grid model—I. Model formulation

https://www.acert.cornell.edu/PDFs/JMagnReson177_184_2005.pdf

Maximum entropy: A complement to Tikhonov regularization for determination of pair distance distributions by pulsed ESR

Distribution of event times in time-resolved fluorescence: the exponential series approach—algorithm, regularization, analysis

In continuous casting of steel, the solidification process can be influenced by external cooling and by the casting speed. We describe an algorithm based on nonlinear constrained optimization which computes values of these control variables such that a desirable solidification front is approximated within an accuracy that is sufficient for practical purposes.

Numerical solution of an inverse problem connected with continuous casting of steel

After describing the technical background that led to the inverse problem for a nonlinear heat equation considered in this paper, we prove existence, uniqueness and continuous-dependence results for the direct problem, uniqueness for the inverse problem and show how the stability can be restored in the inverse problem by a suitable a-priori bound.

On an Inverse Problem for a Nonlinear Heat Equation Connected with Continuous Casting of Steel

In the production of rolled steel, there are two possible process routes between steel making and hot rolling. The older process is “block casting”, the newer one is “continuous casting”. The latter process has many advantages over the former: First,the resulting product is already in a form usable for the final rolling process, an intermediate rolling process is saved. Ideally, it can be rolled directly after leaving the casting machine (“direct rolling”), which saves the enormous amounts of energy used in the pusher furnace for reheating the steel slabs (cf. the article by Auzinger and Wacker in this volume). Also, in block casting, some of the material at the top and at the bottom of the blocks has to be cut off because of impurities. The relation between usable cast steel and used liquid steel is about 10% better in continuous casting compared to block casting. In the VOEST-Alpine steel company in Linz, for which we carried out the project to be described here, about 90% of the steel is processed by continuous casting.

Thomas Langthaler

Papers

Distribution of event times in time-resolved fluorescence: the exponential series approach—algorithm, regularization, analysis

Numerical solution of an inverse problem connected with continuous casting of steel

On an Inverse Problem for a Nonlinear Heat Equation Connected with Continuous Casting of Steel

Control of the Solidification Front by Secondary Cooling in Continuous Casting of Steel