38 citations · 63 across the 20 of their papers we have counts for
20 papers
Analysis of a nonisothermal and conserved phase field system with inertial term
Pierluigi Colli, Shunsuke Kurima
This paper deals with a conserved phase field system that couples the energy balance equation with a Cahn--Hilliard type system including temperature and the inertial term for the…
Nonlocal to local convergence of phase field systems with inertial term
Pierluigi Colli, Shunsuke Kurima, Luca Scarpa
This paper deals with a nonlocal model for a hyperbolic phase field system coupling the standard energy balance equation for temperature with a dynamic for the phase variable: the…
Nonlocal to local convergence of singular phase field systems of conserved type
Shunsuke Kurima
This paper deals with a singular nonlocal phase field system of conserved type.Colli--K.\ [Nonlinear Anal.\ 190 (2020)] have derived existence of solutions to a singular phase fiel…
Existence for a nonlocal Penrose--Fife type phase field system with inertial term
Shunsuke Kurima
This article deals with a nonlocal Penrose-Fife type phase field system with inertial term. We do not know whether we can prove existence of solutions in reference to Colli--Grasse…
Existence for a singular nonlocal phase field system with inertial term
Shunsuke Kurima
In this paper we deal with a singular nonlocal phase field system with inertial term. The system has the logarithm of the absolute temperature under time derivative. Although t…
Time discretization of a nonlocal phase-field system with inertial term
Shunsuke Kurima
Time discretizations of phase-field systems have been studied. For example, a time discretization and an error estimate for a parabolic-parabolic phase-field system have been studi…
Convergence of a Cahn-Hilliard type system to a parabolic-elliptic chemotaxis system with nonlinear diffusion
Shunsuke Kurima
This paper deals with a parabolic-elliptic chemotaxis system with nonlinear diffusion. It was proved that there exists a solution of a Cahn-Hilliard system as an approximation of a…
Time discretization of an abstract problem applying to the linearized equations of coupled sound and heat flow
Shunsuke Kurima
In this paper we deal with an abstract problem which includes the linearized equations of coupled sound and heat flow as an example. Recently, a time discretization of a simultaneo…
Time discretization of an initial value problem for a simultaneous abstract evolution equation applying to parabolic-hyperbolic phase-field systems
Shunsuke Kurima
This article deals with a simultaneous abstract evolution equation. This includes a parabolic-hyperbolic phase-field system as an example which consists of a parabolic equation for…
Global existence for a phase separation system deduced from the entropy balance
Pierluigi Colli, Shunsuke Kurima
This paper is concerned with a thermomechanical model describing phase separation phenomena in terms of the entropy balance and equilibrium equations for the microforces. The relat…
Time discretization of a nonlinear phase field system in general domains
Pierluigi Colli, Shunsuke Kurima
This paper deals with the nonlinear phase field system \begin{equation*} \begin{cases} \partial_t (θ+\ell φ) - Δθ= f & \mbox{in}\ Ω\times(0, T), \\[1mm] \partial_t φ- Δφ+ ξ+ π(φ) =…
Asymptotic analysis for Cahn--Hilliard type phase field systems related to tumor growth in general domains
Shunsuke Kurima
This article considers a limit system by passing to the limit in the following Cahn--Hilliard type phase field system related to tumor growth as : \begin{equation*} \be…
Existence and energy estimates of weak solutions for nonlocal Cahn--Hilliard equations on unbounded domains
Shunsuke Kurima
This paper considers the initial-boundary value problem for the nonlocal Cahn--Hilliard equation $$ \partial_tφ+ (-Δ+1)(a(\cdot)φ-J\astφ+ G'(φ)) = 0 \quad \mbox{in}\ Ω\times(0, T)…
Global weak solutions to a 3-dimensional degenerate and singular chemotaxis-Navier--Stokes system with logistic source
Shunsuke Kurima, Masaaki Mizukami
This paper considers the degenerate and singular chemotaxis-Navier--Stokes system with logistic term , $x \in Ω,\ t…
Nonlinear diffusion equations as asymptotic limits of Cahn--Hilliard systems on unbounded domains via Cauchy's criterion
Takeshi Fukao, Shunsuke Kurima, Tomomi Yokota
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 e…
Boundedness and stabilization in a three-dimensional two-species chemotaxis-Navier--Stokes system with competitive kinetics
Misaki Hirata, Shunsuke Kurima, Masaaki Mizukami +1
This paper is concerned with the 3-dimensional two-species chemotaxis-Navier--Stokes system with Lotka--Volterra competitive kinetics under homogeneous Neumann boundary conditions…
Global existence and asymptotic behavior of classical solutions for a 3D two-species Keller--Segel-Stokes system with competitive kinetics
Xinru Cao, Shunsuke Kurima, Masaaki Mizukami
This paper deals with the two-species Keller--Segel-Stokes system with competitive kinetics $(n_1)_t + u\cdot\nabla n_1 =Δn_1 - χ_1\nabla\cdot(n_1\nabla c)+ μ_1n_1(1- n_1 - a_1n_2)…
A direct approach to quasilinear parabolic equations on unbounded domains by Brézis's theory for subdifferential operators
Shunsuke Kurima, Tomomi Yokota
This paper is concerned with existence and uniqueness of solutions to two kinds of quasilinear parabolic equations. One is described as the form which includes the porous media and…
Global existence and asymptotic behavior of classical solutions for a 3D two-species chemotaxis-Stokes system with competitive kinetics
Xinru Cao, Shunsuke Kurima, Masaaki Mizukami
This paper considers the two-species chemotaxis-Stokes system with competitive kinetics under homogeneous Neumann boundary conditions in a three-dimensional bounded domain with smo…
Nonlinear diffusion equations as asymptotic limits of Cahn-Hilliard systems
Pierluigi Colli, Takeshi Fukao
An asymptotic limit of a class of Cahn-Hilliard systems is investigated to obtain a general nonlinear diffusion equation. The target diffusion equation may reproduce a number of we…