Analysis and Numerics of Partial Differential Equations by Franco Brezzi (auth.), Franco Brezzi, Piero Colli Franzone,

By Franco Brezzi (auth.), Franco Brezzi, Piero Colli Franzone, Ugo Gianazza, Gianni Gilardi (eds.)

This quantity is a range of contributions provided via pals, collaborators, prior scholars in reminiscence of Enrico Magenes. the 1st half provides a large old point of view of Magenes' paintings in his 50-year mathematical profession; the second one half comprises unique study papers, and indicates how rules, tools, and strategies brought by way of Magenes and his collaborators nonetheless influence the present study in Mathematics.

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2 Stefan Problems in a Concentrated Capacity The Stefan problems in a concentrated capacity [24] arise in heat diffusion phenomena involving phase changes in two adjoining bodies Ω and Γ , when assuming that the thermal conductivity along the direction normal to the boundary of Ω is much greater than in the others, whence Γ can be considered as the boundary of Ω. The mathematical model describing phase change process in both bodies reads [42]: ∂β(u) ∂u − g β(u) = on ∂Ω × (0, T ), ∂t ∂ν on ∂Ω, ⎧ u(·, 0) = u0 (·) ∂v ⎪ ⎪ − γ (v) = 0 in Ω × (0, T ), ⎨ ∂t v(·, 0) = v0 (·) in Ω, ⎪ ⎪ ⎩ γ (v) = β(u) on ∂Ω × (0, T ), (7) where g is the Laplace-Beltrami operator on ∂Ω with respect to the Riemannian structure g inferred by the tangential conductivity, β and γ are the constitutive relations between enthalpies u and v and temperature θ = β(u) = γ (v).

14. Gakkötosho, Tokyo (2000) 32. : Regularity in free boundary problems. Ann. Sc. Norm. Super. Pisa, Cl. Sci. (4) 4, 373–391 (1977) 33. Magenes, E. ): Free Boundary Problems. Istituto Nazionale di Alta Matematica, Roma (1980) 34. : Problemi di Stefan bifase in più variabili spaziali. Matematiche XXXVI, 65–108 (1981) 35. : Remarques sur l’approximation des problèmes paraboliques non linéaires. In: Analyse Mathématique et Applications. Contributions en l’honneur de Jacques-Louis Lions, pp. 297–318.

Numer. Methods Eng. 26, 1989–2007 (1988) 78. : Convergence of the approximate free boundary for the multidimensional one-phase Stefan problem. Comput. Mech. 1, 115–125 (1986) 79. : On the determination of the position of the boundary which separates two phases in the one-dimensional problem of Stefan. Dokl. Acad. Nauk USSR 58, 217–220 (1947) 80. : The Stefan Problem. Translations of Mathematical Monographs, vol. 27. Am. Math. , Providence (1971) 81. : Optimal rates of convergence for degenerate parabolic problems in two dimensions.

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