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  • 1
    Electronic Resource
    Electronic Resource
    The one-phase Stefan problem for the heat equation with boundary temperature specification (1970)
    Springer
    Archive for rational mechanics and analysis 39 (1970), S. 270-274 
    Details
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00281365
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  • 2
    Electronic Resource
    Electronic Resource
    Regularity of weak solutions of one-dimensional two-phase Stefan problems (1977)
    Springer
    Annali di matematica pura ed applicata 115 (1977), S. 341-348 
    Details
    ISSN: 1618-1891
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Sunto Si considera il problema di Stefan unidimensionale a due fasi e si dimostra l'esistenza di soluzioni classiche sotto ipotesi minimali sui dati (continuità a tratti e limitatezza). Nelle stesse ipotesi si dimostra che tali soluzioni dipendono in modo continuo dai dati, conseguendo un risultato che è più generale anche di quello noto per le soluzioni deboli.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02414725
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  • 3
    Electronic Resource
    Electronic Resource
    Combustion with phase transition (1993)
    Springer
    Meccanica 28 (1993), S. 185-194 
    Details
    ISSN: 1572-9648
    Keywords: Combustion ; Reaction-diffusion ; Phase transition ; Free boundary problem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Description / Table of Contents: Sommario Si studia il problema matematico che descrive una reazione chimica esotermica in una sostanza che diffonde e puo' subire cambiamenti di fase. Si dimostra esistenza globale in senso classico del relativo sistema di equazioni alle derivate parziali e si discute la possibilita' che le fasi siano separate da una regione di transizione e non da una netta superficie di interfase. Il caso limite di assenza di diffusione e' anche brevemente esaminato.
    Notes: Abstract The paper deals with a mathematical problem describing an exothermic chemical reaction in a diffusing substance possibly undergoing a change of phase. Global well-posedness in the classical sense is proved for the corresponding system of PDEs. Moreover, cases in which the phases are separated by sharp interphases or by transition regions are discussed. The limit case of negligible diffusion is also considered.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00989120
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  • 4
    Electronic Resource
    Electronic Resource
    Book reviews (1993)
    Springer
    Meccanica 28 (1993), S. 257-262 
    Details
    ISSN: 1572-9648
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00989129
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  • 5
    Electronic Resource
    Electronic Resource
    Book reviews (1995)
    Springer
    Meccanica 30 (1995), S. 735-738 
    Details
    ISSN: 1572-9648
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00986578
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  • 6
    Electronic Resource
    Electronic Resource
    Stefan — like problems with space — dependent latent heat (1970)
    Springer
    Meccanica 5 (1970), S. 187-190 
    Details
    ISSN: 1572-9648
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Description / Table of Contents: Summary A wide class of one-dimensional heat conduction problems with phase change is considered on the assumption that the latent heat is a given function of the position of the separation plane between the two phases: L=φ[s(t)]. Some sufficient conditions for the existence and uniqueness of the solution in a given time-interval are given. This work permits the generalization of some previous results and the investigation of some cases of particular interest.
    Notes: Sommario Si studia una vasta classe di problemi di conduzione unidimensionale del calore in presenza di cambiamento di fase, nel caso in cui il calore latente sia funzione della posizione del fronte di separazione tra le due fasi: L=φ[s(t)]. Si trovano delle condizioni sufficienti per l'esistenza e la unicità della soluzione del problema in un certo intervallo di tempo; si mostra infine che la trattazione permette di generalizzare risultati già noti e di estendere lo studio a casi di particolare interesse.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02133573
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  • 7
    Electronic Resource
    Electronic Resource
    An efficient method for solving free-boundary diffusion problems (1973)
    Springer
    Meccanica 8 (1973), S. 223-235 
    Details
    ISSN: 1572-9648
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Description / Table of Contents: Summary A new method is introduced for solving free-boundary problems for the heat equation. The method is shown to be uniformly convergent both for first type and nonlinear second type boundary conditions. Approximate solutions are obtained by discretization of the time variable and recursive solution at each time step of classical heat conduction linear problems in slabs of known thickness. An error estimate is given. Numerical tests are presented in a few cases in which exact solutions are known.
    Notes: Sommario Si introduce un nuovo metodo per la soluzione di problemi a contorno libero per l'equazione del calore. Si dimostra la convergenza uniforme del metodo sia per condizioni al contorno del primo tipo che per condizioni al contorno del secondo tipo non lineari. Le soluzioni approssimate sono ottenute discretizzando la variabile temporale e risolvendo ricorsivamente ad ogni passo un classico problema lineare di conduzione in uno strato di spessore noto. E' data una stima dell'errore. Per alcuni casi nei quali è nota la soluzione esatta sono presentate prove numeriche.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02342408
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  • 8
    Electronic Resource
    Electronic Resource
    A two phase Stefan problem with temperature boundary conditions (1971)
    Springer
    Annali di matematica pura ed applicata 88 (1971), S. 177-191 
    Details
    ISSN: 1618-1891
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Description / Table of Contents: Abstract We studied a two phase Stefan problem in a infinite plane slab, when the temperatures are prescribed on the two limiting planes. We proved global existence and uniqueness of the solution under minimal smoothness assumptions upon the initial and boundary data. Furthermore, we demonstrated the continuous and monotone dependence of the solution on the initial and boundary data.
    Notes: Riassunto Si studia un problema di Stefan a due fasi in uno strato piano indefinito, quando sia assegnata la temperatura sui piani che delimitano lo strato stesso. Viene dimostrata l’esistenza (in grande) e l’unicità della soluzione sotto ipotesi assai generali sui dati iniziali ed al contorno. Sî prova la dipendenza continua e monotona della soluzione dai dati iniziali ed al contorno.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02415066
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  • 9
    Electronic Resource
    Electronic Resource
    A two phase Stefan problem with flux boundary conditions (1971)
    Springer
    Annali di matematica pura ed applicata 88 (1971), S. 193-205 
    Details
    ISSN: 1618-1891
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Description / Table of Contents: Abstract We studied a two phase Stefan problem in a infinite plane slab, when the thermal fluxes are assigned on the two limiting planes. We proved existence and uniqueness of the solution upon minimal smoothness assumptions upon the initial and boundary data, and we demonstrated the continuous and monotone dependence of the solution on the data. In sec. 5 we studied in which cases one of the two phases disappears and the asymptotic behavior in the cases in which the two phases exist for all time.
    Notes: Riassunto Si studia un problema di Stefan a due fasi in uno strato piano indefinito quando si suppongono assegnati i flussi termici sui piani che delimitano lo strato stesso. Viene dimostrata l’esistenza e l’unicità della soluzione con ipotesi assai generali sui dati iniziali ed al contorno del problema, nonchè la dipendenza continua e monotona della soluzione da tali dati. Si esaminano infine i casi in cui una delle due fasi può sparire ed il comportamento asintotico in caso di permanenza delle due fasi.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02415067
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  • 10
    Electronic Resource
    Electronic Resource
    Homogenization of the heat equation for a domain with a network of pipes with a well-mixed fluid (1994)
    Springer
    Annali di matematica pura ed applicata 166 (1994), S. 227-251 
    Details
    ISSN: 1618-1891
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider the linear heat equation in a domain occupied by a solid material with a network of pipes in which a well-mixed fluid is circulating. The temperature of the fluid in the pipe is uniform and its time variation is determined by the thermal flux on the wall of the pipe, plus a given internal source; continuity of the temperature across the pipe is also assumed. We suppose that we deal with a periodic geometry, with cells of size ε with inclusions of size rg; we study in detail in the case rε∼ε, referring to a previous paper for the case rε≪ε In the limit ε»0 we get a homogenized equation. The limit depends strongly on the ratio between the time variation of the temperature in the inclusions and the thermal flux through the interface. The homogenized equation has a new specific heat, which depends on the porosity and the constant of proportionality between the time variation of temperature and the flux on the boundary of the pipe. We also have a new thermal conductivity depending on the microstructure, and volume sources appear. The main tool is the energy method and we generalize the classical results for the more standard boundary conditions for parabolic equations. Finally, we consider the network of pipes forming a random ball structure. We prove convergence for this case. The homogenized equation is of the same form as in the periodic case but auxiliary problems are stochastic.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01765636
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