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research article
The Allen-Cahn equation with generic initial datum
April 8, 2023
We consider the Allen-Cahn equation ?(t)u - ?u = u - u(3) with a rapidly mixing Gaussian field as initial condition. We show that provided that the amplitude of the initial condition is not too large, the equation generates fronts described by nodal sets of the Bargmann-Fock Gaussian field, which then evolve according to mean curvature flow.
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Name
s00440-023-01198-5.pdf
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Publisher's version
Access type
openaccess
License Condition
CC BY
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584.62 KB
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Adobe PDF
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eb01ddb95c1863ad324ad6a329288941