Analysis of a mixture model of tumor growth

作者：Lowengrub John^*; Titi Edriss; Zhao Kun

来源：European Journal of Applied Mathematics, 2013, 24: 691-734.

DOI：10.1017/S0956792513000144

• Cahn-Hilliard-Hele-Shaw equation
• Global existence and uniqueness
• Regularity
• Gevrey class regularity
• Long-time asymptotic behaviour

We study an initial-boundary value problem for a coupled Cahn-Hilliard-Hele-Shaw system that models tumour growth. For large initial data with finite energy, we prove global (local resp.) existence, uniqueness, higher order spatial regularity and the Gevrey spatial regularity of strong solutions to the initial-boundary value problem in two dimensions (three dimensions resp.). Asymptotically in time, we show that the solution converges to a constant state exponentially fast as time tends to infinity under certain assumptions.

• 出版日期2013-10