Analysis of a Mixture Model of Tumor Growth

2012/05/30 by John Lowengrub, Lowengrub, John, Edriss S. Titi +3 · 1 citation
Earth and Planetary Sciences · Materials Science · Mathematics · #35B40 #35B65 #35Q35 #Analysis of PDEs (math.AP) #Biological Physics (physics.bio-ph) #FOS: Biological sciences #FOS: Mathematics #FOS: Physical sciences #Pattern Formation and Solitons (nlin.PS) #Quantitative Methods (q-bio.QM) #Solidification and crystal growth phenomena #Stochastic processes and statistical mechanics #nanoparticles nucleation surface interactions

paper · pdf · doi:10.48550/arxiv.1205.6780

openalex publication_date 2012/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 (local resp.) existence, uniqueness, higher order spatial regularity and Gevrey spatial regularity of strong solutions to the IBVP in 2D (3D resp.). Asymptotically in time, we show that the solution converges to a constant state exponentially fast as time tends to infinity under certain assumptions.

Citations

• Gevrey class regularity for the solutions of the Navier-Stokes equations
• Three-dimensional multispecies nonlinear tumor growth—II: Tumor invasion and angiogenesis

Cited by

• Local Well-Posedness of the Cahn-Hilliard-Biot System

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