Shunsuke Kurima

Nonlinear diffusion equations as asymptotic limits of Cahn-Hilliard systems on unbounded domains via Cauchy's criterion: Nonlinear diffusion equations as asymptotic limits of Cahn-Hilliard systems on unbounded domains via Cauchy's criterion

This paper develops an abstract theory for subdifferential operators to give existence and uniqueness of solutions to the initial-boundary problem (P) for the nonlinear diffusion equation in an unbounded domain

Global existence and asymptotic behavior of classical solutions for a 3D two-species chemotaxis-Stokes system with competitive kinetics: Global existence and asymptotic behavior of classical solutions for a 3D two-species chemotaxis-Stokes system with competitive kinetics

\Omega\subset\mathbb{R}^N

Boundedness and stabilization in a two-dimensional two-species chemotaxis-Navier–Stokes system with competitive kinetics

(

Global existence and asymptotic behavior of classical solutions for a 3D two-species Keller--Segel-Stokes system with competitive kinetics

N\in{\mathbb N}

A direct approach to quasilinear parabolic equations on unbounded domains by Br\'ezis's theory for subdifferential operators

), written as \[ \frac{\partial u}{\partial t} + (-\Delta+1)\beta(u) = g \quad \mbox{in}\ \Omega\times(0, T), \] which represents the porous media, the fast diffusion equations, etc., where

Monotonicity methods for nonlinear diffusion equations and their approximations with error estimates

\beta

Global weak solutions to a 3-dimensional degenerate and singular chemotaxis–Navier–Stokes system with logistic source

is a single-valued maximal monotone function on

Existence and energy estimates of weak solutions for nonlocal Cahn--Hilliard equations on unbounded domains.

\mathbb{R}

Asymptotic analysis for Cahn--Hilliard type phase field systems related to tumor growth in general domains

, and

Boundedness and stabilization in a three-dimensional two-species chemotaxis-Navier-Stokes system

T>0