The dynamics of pattern selection for the Cahn-Hilliard equation

摘要: The Cahn-Hilliard equation is a fourth-order parabolic partial differential which one of the leading models for study phase separation in isothermal, isotropic mixtures. goal this dissertation to provide insight into qualitative dynamic properties solutions one-dimensional equation. main focus on early stages evolution whose initial data nearly uniform. Linear and numerical analysis has led conjecture existence large class such that evolve relatively quickly become periodic with amplitude small period. Such would correspond experimentally-observed phenomenon spinodal decomposition, fine-grained decomposition molten binary alloy after it been rapidly quenched. In dissertation, I present rigorous mathematical justification process decomposition. believe first treatment phenomenon. As complement these precise results, last part deals certain formal asymptotic methods studying aspects have not yet settled by techniques. particular, approximate finite system ordinary equations are derived various contexts, their behavior described.