By et al Pierluigi Colli (Editor)
ISBN-10: 9812566503
ISBN-13: 9789812566508
Part transition phenomena come up in various proper actual international events, resembling melting and freezing in a solid–liquid approach, evaporation, solid–solid section transitions suit reminiscence alloys, combustion, crystal development, harm in elastic fabrics, glass formation, section transitions in polymers, and plasticity. the sensible curiosity of such phenomenology is obvious and has deeply encouraged the technological improvement of our society, stimulating excessive mathematical study during this quarter. This e-book analyzes and approximates a few types and comparable partial differential equation difficulties that contain part transitions in several contexts and contain dissipation results.
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Sample text
In fi, (95) and Uoo = | f i r 1 ( m + c0) (96) follows via (86), so that the implication (b) is proved. Conversely, assuming (94) yields (95), hence (96). Thus, in this case (94) actually corresponds to | f t | l o g 0 c > ( m + co). (97) In particular, we have if |ft|log0 c < (m + c0) then Uoo > log0 c . e. if m + co > |fl|log# c > m + c0 — |fi| necessarily we have Moo = log0 c , and by (86) Jn Xoo = rn + Co - \Cl\ log0 c . This concludes the proof of Theorem 6. Phase transitions and entropy equation: long-time behaviour of solutions 41 Acknowledgments T h e author would like to t h a n k the referee for his/her detailed remarks, which surely contributed to improve the final version of the paper.
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E. Gurtin, Equipresence and constitutive equations for rigid heat conductors. Z. Angew. Math. Phys. 18, 199-208 (1967). [12] P. Colli, G. Gilardi and M. Grasselli, Well-posedness of the weak formulation for the phase-field model with memory. Adv. Differential Equations 2, 487-508 (1997). [13] P. Colli and Ph. Laurencot, Existence and stabilization of solutions to the phase-field model with memory. J. Integral Equations Appl. 10, 169-193 (1998). [14] P. Colli, F. Luterotti, G. Schimperna and U. Stefanelli, Global existence for a class of generalized systems of irreversible phase changes.
Dissipative Phase Transitions by et al Pierluigi Colli (Editor)
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