Phase Transitions and Hysteresis [electronic resource] : Lectures given at the 3rd Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Montecatini Terme, Italy, July 13–21, 1993 / by M. Brokate, Yong Zhong Huo, Noboyuki Kenmochi, Ingo Müller, José F. Rodriguez, Claudio Verdi ; edited by Augusto Visintin.
Material type: TextSeries: Lecture Notes in Mathematics ; 1584Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 1994Description: VIII, 296 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783540486787Subject(s): Mathematics | Global analysis (Mathematics) | Numerical analysis | Mathematical physics | Mechanics | Mechanics, applied | Mathematics | Analysis | Mathematical and Computational Physics | Numerical Analysis | Mechanics | Theoretical and Applied MechanicsAdditional physical formats: Printed edition:: No titleDDC classification: 515 LOC classification: QA299.6-433Online resources: Click here to access onlineCurrent library | Home library | Call number | Materials specified | URL | Status | Date due | Barcode |
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Hysteresis operators -- Systems of nonlinear PDEs arising from dynamical phase transitions -- Quasiplasticity and pseudoelasticity in shape memory alloys -- Variational methods in the stefan problem -- Numerical aspects of parabolic free boundary and hysteresis problems.
1) Phase Transitions, represented by generalizations of the classical Stefan problem. This is studied by Kenmochi and Rodrigues by means of variational techniques. 2) Hysteresis Phenomena. Some alloys exhibit shape memory effects, corresponding to a stress-strain relation which strongly depends on temperature; mathematical physical aspects are treated in Müller's paper. In a general framework, hysteresis can be described by means of hysteresis operators in Banach spaces of time dependent functions; their properties are studied by Brokate. 3) Numerical analysis. Several models of the phenomena above can be formulated in terms of nonlinear parabolic equations. Here Verdi deals with the most updated approximation techniques.
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