Under an energy convergence hypothesis, solutions of a heterogeneous Allen-Cahn equation with space-dependent wells converge to a BV solution of weighted mean curvature flow, and a weak-strong uniqueness principle holds.
Stability of multiphase mean curvature flow beyond circular topology changes
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
We prove a weak-strong uniqueness principle for varifold-BV solutions to planar multiphase mean curvature flow beyond a circular topology change: Assuming that there exists a classical solution with an interface that becomes increasingly circular and shrinks to a point, any varifold-BV solution with the same initial interface must coincide with it, and any varifold-BV solution with similar initial data must undergo the same type of topology change. Our result illustrates the robustness of the relative energy method for establishing weak-strong uniqueness principles for interface evolution equations, showing that it may also be applied beyond certain topological changes.
fields
math.AP 1years
2024 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
Convergence of a heterogeneous Allen-Cahn equation to weighted mean curvature flow
Under an energy convergence hypothesis, solutions of a heterogeneous Allen-Cahn equation with space-dependent wells converge to a BV solution of weighted mean curvature flow, and a weak-strong uniqueness principle holds.