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Phase Transitions and Symmetry Breaking in Singular Diffusion

Jochen Denzler and Robert J. McCann
Proceedings of the National Academy of Sciences of the United States of America
Vol. 100, No. 12 (Jun. 10, 2003), pp. 6922-6925
Stable URL: http://www.jstor.org/stable/3139407
Page Count: 4
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Phase Transitions and Symmetry Breaking in Singular Diffusion
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Abstract

The long-time asymptotics are determined for fast nonlinear diffusion by linearizing Otto's gradient descent model at the Barenblatt profile. The spectrum of the entropy is explicitly determined. The dynamics are found to undergo a phase transition in which rotational symmetry is broken as the strength of the nonlinearity is varied.

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