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Energy Stable and Efficient Finite-Difference Nonlinear Multigrid Schemes for the Modified Phase Field Crystal Equation
Arvind Baskaran, Peng Zhou, Zhengzheng Hu +3
In this paper we present two unconditionally energy stable finite difference schemes for the Modified Phase Field Crystal (MPFC) equation, a sixth-order nonlinear damped wave equat…
Convergence Analysis of a Second Order Convex Splitting Scheme for the Modified Phase Field Crystal Equation
Arvind Baskaran, John Lowengrub, Cheng Wang +1
In this paper we provide a detailed convergence analysis for an unconditionally energy stable, second-order accurate convex splitting scheme for the Modified Phase Field Crystal eq…
Analysis of a Mixture Model of Tumor Growth
John Lowengrub, Edriss S. Titi, Kun Zhao
We study an initial-boundary value problem (IBVP) for a coupled Cahn-Hilliard-Hele-Shaw system that models tumor growth. For large initial data with finite energy, we prove global…