LEADER 05540nam 22007214a 450 001 9910451906403321 005 20200520144314.0 010 $a1-281-37888-7 010 $a9786611378882 010 $a981-277-429-7 035 $a(CKB)1000000000480113 035 $a(EBL)1679506 035 $a(OCoLC)879023553 035 $a(SSID)ssj0000140055 035 $a(PQKBManifestationID)11154915 035 $a(PQKBTitleCode)TC0000140055 035 $a(PQKBWorkID)10029366 035 $a(PQKB)11134530 035 $a(MiAaPQ)EBC1679506 035 $a(WSP)00006020 035 $a(Au-PeEL)EBL1679506 035 $a(CaPaEBR)ebr10201337 035 $a(CaONFJC)MIL137888 035 $a(EXLCZ)991000000000480113 100 $a20051223d2006 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 00$aDissipative phase transitions$b[electronic resource] /$feditors, Pierluigi Colli, Nobuyuki Kenmochi, Ju?rgen Sprekels 210 $aHackensack, N.J. $cWorld Scientific$dc2006 215 $a1 online resource (321 p.) 225 1 $aSeries on advances in mathematics for applied sciences,$x1793-0901 ;$vv. 71 300 $aDescription based upon print version of record. 311 $a981-256-650-3 320 $aIncludes bibliographical references. 327 $aCONTENTS ; Preface ; Mathematical models including a hysteresis operator ; 1 Introduction ; 2 Mathematical treatment for hysteresis operator ; 2.1 Play operator ; 2.2 Stop operator ; 2.3 The Duhem model ; 3 Shape memory alloys ; 4 Examples of hysteresis operator 327 $a4.1 Solid-liquid phase transition 4.2 Biological model ; 4.3 Magnetostrictive thin film multi-layers ; References ; Modelling phase transitions via an entropy equation: long-time behaviour of the solutions ; 1 Introduction ; 2 The model and the resulting PDE's system ; 3 Main results 327 $a4 The existence and uniqueness result 4.1 Proof of Theorem 5 ; 5 Uniform estimates on (0. +oo) ; 6 The w-limit ; References ; Global solution to a one dimensional phase transition model with strong dissipation ; 1 Introduction and derivation of the model ; 2 Notation and main results 327 $a3 Proof of Theorem 1 4 Proof of Theorem 2 ; References ; A global in time result for an integro-differential parabolic inverse problem in the space of bounded functions ; 1 Introduction ; 2 Definitions and main results ; 2.1 The main abstract result ; 2.2 An application 327 $a3 The weighted spaces 4 An equivalent fixed point system ; 5 Proof of Theorem 6 ; References ; Weak solutions for Stefan problems with convections ; 1 Introduction ; 2 Stefan problem in non-cylindrical domain with convection governed by Navier-Stokes equations 327 $a2.1 Classical formulation 330 $aPhase transition phenomena arise in a variety of relevant real world situations, such as melting and freezing in a solid-liquid system, evaporation, solid-solid phase transitions in shape memory alloys, combustion, crystal growth, damage in elastic materials, glass formation, phase transitions in polymers, and plasticity. The practical interest of such phenomenology is evident and has deeply influenced the technological development of our society, stimulating intense mathematical research in this area. This book analyzes and approximates some models and related partial differential equation 410 0$aSeries on advances in mathematics for applied sciences ;$vv. 71. 606 $aPhase transformations (Statistical physics) 606 $aPhase transformations (Statistical physics)$xMathematical models 606 $aEnergy dissipation 608 $aElectronic books. 615 0$aPhase transformations (Statistical physics) 615 0$aPhase transformations (Statistical physics)$xMathematical models. 615 0$aEnergy dissipation. 676 $a530.4/74 701 $aColli$b P$g(Pierluigi),$f1958-$021039 701 $aKenmochi$b Nobuyuki$0974272 701 $aSprekels$b J$027708 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910451906403321 996 $aDissipative phase transitions$92218011 997 $aUNINA