Title & Abstract

Abstract: This talk deals with a special case of a quasilinear fully parabolic attraction-repulsion chemotaxis system in the two- or three-dimensional setting. The main result of this talk asserts finite-time blow-up by using a Lyapunov type functional in this system. This is based on a joint work [1]. The result indeed has already been observed by [2] earlier than [1].

References 

[1] Y. Chiyo, T. Uemura and T. Yokota, Finite-time blow-up in a quasilinear fully parabolic attraction-repulsion chemotaxis system with density-dependent sensitivity, Electron. J. Differential Equations 2025 (2025), Paper No. 81, 10 pp.

[2] S. Frassu and J. Lankeit, Private discussion (2025).

Abstract: In this talk, we investigate the unsteady motion of incompressible chemically reacting generalized Newtonian fluids where the power-law index depends on the concentration, which satisfies the convection-diffusion equation. We establish the existence and uniqueness of global-in-time strong solutions for relatively high power-law indices. Furthermore, we establish the well-posedness of local strong solutions in the shear-thinning (power-law index less than 2) regime. 

Abstract: In this talk, we consider the quasilinear Keller--Segel system with critical nonlinearity. In the study of large time behaviour of solutions to the system, its entropy functional plays an important role. On the other hand, in the one-dimensional case, the entropy structure has a poor information. In stead of the entropy, we focus on the entropy production of the system and derive its estimate.

Abstract: In this presentation, we discuss recent existence results for nonlinear diffusion equations with drift terms in divergence form.

These results are broadly applicable to a variety of reaction diffusion models, including Keller Segel models.

We emphasize the identification of functional spaces for the drift term, guided by the diffusion nonlinearity and the regularity of the initial data.

Abstract: 

Abstract: In this talk, we discuss a higher integrability result for very weak solutions, which have lower integrability than standard weak solutions, of elliptic systems with nonstandard growth. This result generalizes the recent work by Baasandorj, Byun and Kim (Trans. Amer. Math. Soc., 2023) with respect to the derivative order and related structural conditions. The key ingredients are a higher-order Lipschitz truncation adapted to the double phase structure and Sobolev--Poincar\'e inequalities associated with the double phase operator.

Abstract: In this talk we consider the asymptotic dynamics of global bounded solutions to a Keller-Segel model with a logistic source and nonlinear gradient-dependent damping. We investigate two cases. First, in the presence of a logistic source, the solution uniformly converges to a unique positive steady state. Second, without the logistic source, the gradient damping strictly drives the solution to a constant state in an appropriate topology, determined by the mass. 

Abstract: In this talk, we consider partial differential equations in the modeling of collective behavior in populations of Bacillus subtilis. We consider the temporal decay estimates of the weak solutions to the Cauchy problem for the modeling in the water drops. Then we consider existence of the solution to some extended modeling describing the interaction of motile B. subtilis and non-motile algae.

Abstract: This talk deals with a tuberculosis granuloma formation model proposed by Feng (2024). Feng (2024) not only proposed the problem but also analyzed the ODE setting of the problem and showed that the reproduction number is important to show properties of solutions. On the other hand, for the PDE setting, there might not be any results. The purpose of this talk is to analyze the PDE setting and to show global existence of solutions to the problem and their grow-up properties.This talk is based on a joint work with Mario Fuest (Leibniz Universität Hannover), Johannes Lankeit (Leibniz Universität Hannover), and that with Yuya Tanaka (Kwansei Gakuin University).

Abstract: In this talk, we prove the global existence of weak solutions to quasilinear Keller–Segel systems with nonlinear mobility by minimizing movements (JKO scheme) in the product space of the weighted Wasserstein space and L2 space. In particular, we newly show the global existence of weak solutions to the Keller—Segel system with the degenerate diffusion in the critical case. The advantage of our approach is that we can connect the global existence of weak solutions to the Keller–Segel systems with the boundedness from below of a suitable functional. While minimizing movements for Keller– Segel systems with linear mobility are adapted in the product space of the Wasserstein space and L2 space, due to the nonlinearity of mobility, we need to use the weighted Wasserstein space instead of the Wasserstein space. Moreover, since the mobility function is not Lipschitz, we first find solutions to the Keller–Segel systems whose mobility is approximated by a Lipschitz function, and then we establish additional uniform estimates and convergences to derive solutions to the Keller–Segel systems.

Abstract: We establish convergence to equilibrium for Wasserstein gradient flows of genuinely nonconvex free energies, motivated by the McKean–Vlasov (granular media) equation.Our approach is based on a Wasserstein–Łojasiewicz gradient inequality for the associated free energy, established under mild analyticity assumptions on the confinement and interaction potentials, which yields asymptotic convergence of any global bounded trajectory without assuming displacement convexity or log-Sobolev/Talagrand-type functional inequalities. As a prominent application, this framework implies convergence to equilibrium for global bounded solutions of the parabolic–elliptic Keller–Segel chemotaxis model on the torus. This is joint work with Beomjun Choi (KAIST) and Seunghoon Jeong (POSTECH).

Abstract: We consider a no-flux initial-boundary value problem for the degenerate volume-filling chemotaxis system with diffusion and chemotactic sensitivity depending on cell densities and signal concentration. We first prove that there exists a global weak solution. Second, under some additional conditions, we show uniqueness of global weak solutions with the mass conservation law. Moreover, we construct a flat-hump-shaped stationary solution in the one-dimensional setting. These results extend the ones in Laurencot-Wrzosek (2005), where they studied a related problem with diffusion and chemotactic sensitivity depending only on cell densities. This is a joint work with Professor Tomomi Yokota (Tokyo University of Science).

Abstract: This talk deals with a model for tuberculosis granuloma formation, which was proposed by Feng in 2024. For this model global existence of classical/weak solutions was established in 2-/3-dimensional settings by Fuest--Lankeit--Mizukami (2025). However, at least two problems remain open: boundedness of the solutions; global existence of classical solutions in three and higher dimensional settings. In this talk I will show not only global existence and boundedness of classical solutions, but also its asymptotic behavior. This is joint work with Masaaki Mizukami (Kyoto Univ. of Edu.).

Abstract: In this talk we consider a class of direct (and indirect) chemotaxis-consumption systems with signal-dependent sensitivity. In previous studies, boundedness of solutions to the system has been obtained under some restrictions on the dimensionand the diffusion coefficient. The purpose of this talk is to remove these restrictions. This is a joint work with KhadijehBaghaei (Pasargad Institute for Advanced Innovative Solutions),YutaroChiyo (Tokyo University of Science) and ChihayaMachino (Tokyo University of Science).

Abstract: We consider a prey–taxis system in which predator movement is regulated indirectly through a signal produced by population interactions. Rather than prescribing a direct taxis term, the model incorporates a signal-dependent dispersal mechanism, allowing the same framework to describe either attractive or avoidance-driven movement depending on the monotonicity of the motility function.Global existence and uniform boundedness of classical solutions in two spatial dimensions are established.The stability of the spatially homogeneous coexistence equilibrium is investigated through linear stability analysis and degree-theoretic arguments, revealing diffusion-driven instabilities induced by interaction-mediated dispersal and the emergence of nonconstant steady states.Numerical simulations are presented to illustrate and complement the theoretical results.