arXiv subjects

Tatsuya Hosono

Publications and source records attributed to Tatsuya Hosono.

4 recordsLinked to original sources

arXiv2026

Global existence and boundedness for a degenerate chemotaxis system with indirect signal production via minimizing movement schemes

Global existence and boundedness of weak solutions for a fully parabolic degenerate chemotaxis system with indirect signal production are proved for any initial data in the subcritical case and under smallness conditions in the critical and supercritical cases. To construct weak solutions, a time discrete scheme is set up, for which the first equation has a gradient flow structure with respect to the 2-Wasserstein distance, while the other two equations feature an L\textsuperscript{2}-variational structure. The proof relies in particular on the flow interchange method and discrete maximal regularity.

math.AP↗

arXiv2026

Global existence for the fully parabolic Keller--Segel system with critical mass on the plane

We study the global existence of solutions to the Cauchy problem for the two-dimensional fully parabolic Keller--Segel system at the critical mass. It is known that global-in-time existence holds for initial data with critical mass under radial symmetry or suitable moment conditions, whereas the behavior of general solutions in the critical regime remains delicate. In this paper, we establish global-in-time existence for general initial data with critical mass, without imposing any symmetry or moment assumptions. The proof relies on the construction of a reconstructed Lyapunov functional, combined with refined regularity estimates for the associated dissipative terms, which enable us to control the solution dynamics in the critical regime.

math.AP↗

arXiv2025

Nonlinear Fisher information, corresponding functional inequalities and applications

We study the evolution of the nonlinear version of the Fisher information along the quasilinear heat equation. We also provide a nonlinear version of a recent functional inequality (Cieślak--Fuest--Hajduk--Sierżęga, 2024), corresponding to the nonlinear heat equation. Next, applications of our version of nonlinear Fisher information to the 1D critical quasilinear fully parabolic Keller--Segel system are given. In particular, the global existence of solutions to the critical nonlinear diffusion/nonlinear sensitivity 1D fully parabolic Keller--Segel system is obtained for certain type of diffusion. Last, but not least, we also study the version of the Fisher information along the $p$-Laplace equation.

math.AP↗

arXiv2024

Global existence and boundedness of solutions to a fully parabolic chemotaxis system with indirect signal production in $\mathbb{R}^4$

Global existence and boundedness of solutions to the Cauchy problem for the four dimensional fully parabolic chemotaxis system with indirect signal production are studied. We prove that solutions with initial mass below $(8π)^2$ exist globally in time. This value $(8π)^2$ is known as the four dimensional threshold value of the initial mass determining whether blow-up of solutions occurs or not. Furthermore, some condition on the initial mass guaranteeing that the solution remains uniformly bounded is also obtained.

math.AP↗