Models of Phase TransitionsSpringer Science & Business Media, 1. dec. 1996 - 326 strani ... "What do you call work?" "Why ain't that work?" Tom resumed his whitewashing, and answered carelessly: "Well. lI1a), he it is, and maybe it aill't. All I know, is, it suits Tom Sawvc/: " "Oil CO/lll!, IIOW, Will do not mean to let 011 that you like it?" The brush continued to move. "Likc it? Well, I do not see wlzy I oughtn't to like it. Does a hoy get a chance to whitewash a fence every day?" That put the thing ill a Ilew light. Ben stopped nibhling the apple .... (From Mark Twain's Adventures of Tom Sawyer, Chapter II.) Mathematics can put quantitative phenomena in a new light; in turn applications may provide a vivid support for mathematical concepts. This volume illustrates some aspects of the mathematical treatment of phase transitions, namely, the classical Stefan problem and its generalizations. The in- tended reader is a researcher in application-oriented mathematics. An effort has been made to make a part of the book accessible to beginners, as well as physicists and engineers with a mathematical background. Some room has also been devoted to illustrate analytical tools. This volume deals with research I initiated when I was affiliated with the Istituto di Analisi Numerica del C.N.R. in Pavia, and then continued at the Dipartimento di Matematica dell'Universita di Trento. It was typeset by the author in plain TEX. |
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V | 6 |
VII | 12 |
VIII | 25 |
IX | 30 |
X | 31 |
XII | 39 |
XIII | 47 |
XV | 54 |
LI | 178 |
LIII | 181 |
LIV | 185 |
LV | 187 |
LVI | 190 |
LVII | 193 |
LVIII | 196 |
LIX | 198 |
XVI | 58 |
XVII | 61 |
XVIII | 65 |
XIX | 68 |
XXI | 74 |
XXII | 78 |
XXIII | 82 |
XXIV | 87 |
XXV | 90 |
XXVII | 96 |
XXVIII | 98 |
XXIX | 100 |
XXX | 104 |
XXXI | 106 |
XXXII | 110 |
XXXIII | 113 |
XXXIV | 117 |
XXXV | 121 |
XXXVI | 123 |
XXXVIII | 131 |
XXXIX | 137 |
XL | 141 |
XLI | 143 |
XLII | 147 |
XLIII | 152 |
XLIV | 155 |
XLVI | 160 |
XLVII | 165 |
XLVIII | 167 |
XLIX | 174 |
L | 176 |
LX | 200 |
LXI | 203 |
LXIII | 208 |
LXIV | 213 |
LXV | 216 |
LXVI | 225 |
LXVII | 227 |
LXVIII | 229 |
LXX | 237 |
LXXI | 239 |
LXXII | 242 |
LXXIII | 242 |
LXXIV | 242 |
LXXV | 242 |
LXXVI | 244 |
LXXVII | 247 |
LXXVIII | 251 |
LXXIX | 252 |
LXXXI | 256 |
LXXXII | 260 |
LXXXIII | 265 |
LXXXIV | 271 |
LXXXV | 277 |
LXXXVI | 280 |
LXXXVII | 282 |
LXXXVIII | 285 |
LXXXIX | 287 |
XC | 289 |
| 311 | |
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Pogosti izrazi in povedi
a.e. in Q analysis approximate assume Banach space Brézis BV(N Chap compactness constant contact angle continuous convergence convex function corresponding defined derived differential Dom(A Dom(P dxdt entropy equation equilibrium equivalent ferromagnetic free boundary free energy fulfilled Gibbs-Thomson law gradient flow heat Hence initial and boundary instance interface L²(N L²(Q Lemma Let us denote Let us set limit linear Lipschitz Lipschitz continuous liquid lower semicontinuous macroscopic maximal monotone graph mean curvature mean curvature flow multiplying mushy region nonconvex nonlinear nucleation parabolic phase transition PNLDE priori estimates Problem 1.1 Proof Proposition prove existence regularity relative minimizers replaced represented Sect sequence Sobolev spaces solid-liquid systems Stefan problem strongly subdifferential subset surface tension temperature Theorem 1.2 thermodynamics undercooling uniformly bounded variational inequality vectorial weak formulation weakly star yields ди
Priljubljeni odlomki
Stran 303 - SL Wang, RF Sekerka, AA Wheeler, BT Murray, SR Coriell, RJ Braun, GB McFadden, Physica D 69, 189 (1993).