Convergence of the Cahn-Hilliard equation to the Hele-Shaw model. (English) Zbl 0828.35105
Summary: We prove that level surfaces of solutions to the Cahn-Hilliard equation tend to solutions of the Hele-Shaw problem under the assumption that classical solutions of the latter exist. The method is based on a new matched asymptotic expansion for solutions, a spectral analysis for linearized operators, and an estimate for the difference between the true solutions and certain approximate ones.
MSC:
| 35Q35 | PDEs in connection with fluid mechanics |
| 35R35 | Free boundary problems for PDEs |
| 76D99 | Incompressible viscous fluids |
Keywords:
level surfaces of solutions; Cahn-Hilliard equation; Hele-Shaw problem; asymptotic expansion for solutions; spectral analysisReferences:
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