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Mathematical issues in combining evolution and Γ-convergence: dangers in phase-field dynamics

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No logo availableBanff International Research Station (BIRS) for Mathematical Innovation and Discovery
 Larsen, Christopher

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Mathematical issues in combining evolution and Γ-convergence: dangers in phase-field dynamics
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19
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Mathematicians have generally not emphasized the difference between Γ-convergence and the convergence necessary for "approximate" dynamic solutions to converge to the correct limiting dynamics. I will discuss what properties limiting dynamic fracture models should have, and how Γ-convergence can fail to deliver them, with an emphasis on phase-field approximations and some surprising problems.