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Energy methods for abstract nonlinear Schrödinger equations

- N. Okazawa, Toshiyuki Suzuki, T. Yokota
- Mathematics
- 1 October 2012

So far there seems to be no abstract formulations
for nonlinear Schrodinger equations (NLS).
In some sense
Cazenave[2, Chapter 3] has given a guiding principle to replace the
free Schrodinger… Expand

Boundedness in quasilinear Keller–Segel systems of parabolic–parabolic type on non-convex bounded domains

- Sachiko Ishida, Kiyotaka Seki, T. Yokota
- Mathematics
- 15 April 2014

Abstract This paper deals with the quasilinear fully parabolic Keller–Segel system { u t = ∇ ⋅ ( D ( u ) ∇ u ) − ∇ ⋅ ( S ( u ) ∇ v ) , x ∈ Ω , t > 0 , v t = Δ v − v + u , x ∈ Ω , t > 0 , under… Expand

Global existence of weak solutions to quasilinear degenerate Keller–Segel systems of parabolic–parabolic type

- Sachiko Ishida, T. Yokota
- Mathematics
- 15 January 2012

Abstract This paper deals with the quasilinear degenerate Keller–Segel system (KS) of parabolic–parabolic type. The global existence of weak solutions to (KS) is established when q m + 2 N (m denotes… Expand

Global existence and smoothing effect for the complex Ginzburg-Landau equation with p-Laplacian

- N. Okazawa, T. Yokota
- Mathematics
- 1 July 2002

Global existence of weak solutions to quasilinear degenerate Keller-Segel systems of parabolic-parabolic type with small data

- Sachiko Ishida, T. Yokota
- Mathematics
- 1 February 2012

This paper deals with the quasilinear degenerate Keller–Segel system (KS) of “parabolic–parabolic” type. The global existence of weak solutions to (KS) with small initial data is established when… Expand

Monotonicity Method Applied to the Complex Ginzburg–Landau and Related Equations

- N. Okazawa, T. Yokota
- Mathematics
- 1 March 2002

Abstract Global existence of unique strong solutions is established for the complex Ginzburg–Landau equation ∂tu − (λ + iα)Δu + (κ + iβ)|u|p − 1u − γu = 0, where λ > 0, κ > 0, α, β, γ ∈ R , p ≥ 1,… Expand

Stabilization in the logarithmic Keller–Segel system

- M. Winkler, T. Yokota
- Mathematics
- 1 May 2018

Abstract The Keller–Segel system u t = D Δ u − D χ ∇ ⋅ ( u v ∇ v ) , x ∈ Ω , t > 0 , v t = D Δ v − v + u , x ∈ Ω , t > 0 , is considered in a bounded domain Ω ⊂ R n , n ≥ 2 , with smooth boundary,… Expand

Stabilization in a chemotaxis model for tumor invasion

- Kentarou Fujie, A. Ito, M. Winkler, T. Yokota
- Physics
- 1 June 2015

This paper deals with the chemotaxis system
\[
\begin{cases}
u_t=\Delta u - \nabla \cdot (u\nabla v),
\qquad x\in \Omega, \ t>0, \\
v_t=\Delta v + wz,
\qquad x\in \Omega, \ t>0, \\
… Expand

Boundedness of solutions to parabolic–elliptic Keller–Segel systems with signal‐dependent sensitivity

- Kentarou Fujie, M. Winkler, T. Yokota
- Mathematics
- 1 April 2015

This paper deals with the parabolic–elliptic Keller–Segel system with signal-dependent chemotactic sensitivity function,
under homogeneous Neumann boundary conditions in a smooth… Expand

Blow-up in finite or infinite time for quasilinear degenerate Keller-Segel systems of parabolic-parabolic type

- Sachiko Ishida, T. Yokota
- Physics
- 1 October 2013

This paper gives a blow-up result for
the quasilinear degenerate Keller-Segel systems
of parabolic-parabolic type.
It is known that
the system has a global solvability in the case where $q < m +… Expand

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