John Lowengrub, Edriss S. Titi, Kun Zhao
Published 2012-05-30Version 1
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.
Initial-boundary value problems for the defocusing nonlinear Schrödinger equation in the semiclassical limit
The initial-boundary value problem for Schrödinger-Korteweg-de Vries system on the half-line
Revisiting Diffusion: Self-similar Solutions and the $t^{-1/2}$ Decay in Initial and Initial-Boundary Value Problems
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