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Classical solutions for a modified Hele‐Shaw model with elasticity
Author(s) -
Abels Helmut,
Schaubeck Stefan
Publication year - 2015
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201400099
Subject(s) - elasticity (physics) , mathematics , mathematical analysis , contraction (grammar) , operator (biology) , physics , medicine , biochemistry , chemistry , repressor , gene , transcription factor , thermodynamics
For a large class of initial data, we prove the existence of classical solutions locally in time to a modified Hele‐Shaw problem that takes elastic effects into account. The system arises as sharp interface model of a Cahn‐Hilliard system coupled with linearized elasticity. By using the Hanzawa transformation, we can reduce the system to a single evolution equation for the height function. Then short time existence is proven by inverting the linearized operator and applying the contraction mapping principle.