On the existence of steady convex solutions to the regularized evolution problem of interfaces in the plane
Authors:
M. Rosati and G. Vergara Caffarelli
Journal:
Quart. Appl. Math. 55 (1997), 151-156
MSC:
Primary 35R35; Secondary 35Q99
DOI:
https://doi.org/10.1090/qam/1433758
MathSciNet review:
MR1433758
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Abstract: In this paper we study some questions arising in the area of multiphase thermomechanics with interfacial structure. In particular, we prove existence and uniqueness results for steady convex solutions to the regularized problem of interfaces in the plane.
- Sigurd Angenent and Morton E. Gurtin, Multiphase thermomechanics with interfacial structure. II. Evolution of an isothermal interface, Arch. Rational Mech. Anal. 108 (1989), no. 4, 323–391. MR 1013461, DOI https://doi.org/10.1007/BF01041068
- Antonio Di Carlo, Morton E. Gurtin, and Paolo Podio-Guidugli, A regularized equation for anisotropic motion-by-curvature, SIAM J. Appl. Math. 52 (1992), no. 4, 1111–1119. MR 1174049, DOI https://doi.org/10.1137/0152065
- Morton E. Gurtin, Thermomechanics of evolving phase boundaries in the plane, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1993. MR 1402243
- Murray H. Protter and Hans F. Weinberger, Maximum principles in differential equations, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1967. MR 0219861
S. Angenent and M. E. Gurtin, Multiphase thermomechanics with interfacial structures. 2 Evolution of an isothermal interface, Arch. Rational Mech. Anal. 108, 323–391 (1989)
A. DiCarlo, M. E. Gurtin, and P. Podio-Guidugli, A regularized equation for anisotropic motionby-curvature, Siam J. Appl. Math. 52, 1111–1119 (1992)
M. E. Gurtin, Thermomechanics of Evolving Phase Boundaries in the Plane, Oxford Science Publications, Clarendon Press, Oxford, 1993
M. H. Protter and H. F. Weinberger, Maximum Principle in Differential Equations, Prentice-Hall, Inc., 1967
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Article copyright:
© Copyright 1997
American Mathematical Society