Traveling phase interfaces in viscous forward-backward diffusion equations
The viscous regularization of an ill-posed diffusion equation with bistable nonlinearity predicts a hysteretic behavior of dynamical phase transitions but a complete mathematical \mbox{understanding} of the intricate multiscale evolution is still missing. We shed light on the fine structure of \mbox...
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Published in | arXiv.org |
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Main Authors | , , |
Format | Paper |
Language | English |
Published |
Ithaca
Cornell University Library, arXiv.org
20.11.2023
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Subjects | |
Online Access | Get full text |
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Summary: | The viscous regularization of an ill-posed diffusion equation with bistable nonlinearity predicts a hysteretic behavior of dynamical phase transitions but a complete mathematical \mbox{understanding} of the intricate multiscale evolution is still missing. We shed light on the fine structure of \mbox{propagating} phase boundaries by carefully examining traveling wave solutions in a special case. Assuming a trilinear constitutive relation we characterize all waves that possess a monotone \mbox{profile} and connect the two phases by a single interface of positive width. We further study the two sharp-interface regimes related to either vanishing viscosity or the bilinear limit. |
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ISSN: | 2331-8422 |