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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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Additional resources for Analysis and Numerics of Partial Differential Equations
2 Stefan Problems in a Concentrated Capacity The Stefan problems in a concentrated capacity  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 : ∂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.