On an integrodifferential equation arising in a theory of phase transitions in solids
Authors:
Rohan Abeyaratne and James K. Knowles
Journal:
Quart. Appl. Math. 55 (1997), 761-767
MSC:
Primary 73B30; Secondary 45J05
DOI:
https://doi.org/10.1090/qam/1486547
MathSciNet review:
MR1486547
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Abstract: This note is concerned with some properties of an integrodifferential equation arising in a continuum model of solid-solid phase transitions.
- Rohan Abeyaratne and James K. Knowles, A continuum model of a thermoelastic solid capable of undergoing phase transitions, J. Mech. Phys. Solids 41 (1993), no. 3, 541–571. MR 1205078, DOI https://doi.org/10.1016/0022-5096%2893%2990048-K
- Rohan Abeyaratne, Sang-Joo Kim, and James K. Knowles, A one-dimensional continuum model for shape-memory alloys, Internat. J. Solids Structures 31 (1994), no. 16, 2229–2249. MR 1287765, DOI https://doi.org/10.1016/0020-7683%2894%2990208-9
- Rohan Abeyaratne and James K. Knowles, Dynamics of propagating phase boundaries: thermoelastic solids with heat conduction, Arch. Rational Mech. Anal. 126 (1994), no. 3, 203–230. MR 1293784, DOI https://doi.org/10.1007/BF00375642
- Rohan Abeyaratne and James K. Knowles, Dynamics of propagating phase boundaries: adiabatic theory for thermoelastic solids, Phys. D 79 (1994), no. 2-4, 269–288. MR 1306463, DOI https://doi.org/10.1016/0167-2789%2894%2990086-8
J. R. Ockendon, Techniques of analysis, in Moving Boundaries in Heat Flow and Diffusion (J. R. Ockendon and W. R. Hodgkins, eds.), Clarendon Press, Oxford, 1975, pp. 138–149
- E. Fried, Stability of a two-phase process involving a planar phase boundary in a thermoelastic solid, Contin. Mech. Thermodyn. 4 (1992), no. 1, 59–79. MR 1150386, DOI https://doi.org/10.1007/BF01126387
R. Abeyaratne and J. K. Knowles, A continuum model of a thermoelastic solid capable of under-going phase transitions, J. Mech. Phys. Solids 41, 541–571 (1993)
R. Abeyaratne, S.-J. Kim, and J. K. Knowles, A one-dimensional continuum model for shape-memory alloys, Internat. J. Solids and Structures 31, 2229–2249 (1994)
R. Abeyaratne and J. K. Knowles, Dynamics of propagating phase boundaries: Thermoelastic solids with heat conduction, Arch. Rational Mech. Anal. 126, 203–230 (1994)
R. Abeyaratne and J. K. Knowles, Dynamics of propagating phase boundaries: Adiabatic theory for thermoelastic solids, Physica D 79, 269–288 (1994)
J. R. Ockendon, Techniques of analysis, in Moving Boundaries in Heat Flow and Diffusion (J. R. Ockendon and W. R. Hodgkins, eds.), Clarendon Press, Oxford, 1975, pp. 138–149
E. Fried, Stability of a two-phase process involving a planar phase boundary in a thermoelastic solid, Continuum Mechanics and Thermodynamics 4, 59–79 (1992)
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Article copyright:
© Copyright 1997
American Mathematical Society