9:20     Opening

9:30 – 10:20   Anna Marciniak-Czochra (Heidelberg University)

Abstract: In this talk, I will present a mechanochemical, PDE-based framework motivated by recent experiments on regenerating epithelia, with Hydra as a model system. The framework couples reaction-diffusion dynamics of a morphogen with elasticity equations governing tissue deformation. A positive feedback between mechanical strain and morphogen production drives symmetry breaking and leads to the emergence of stable, single-peaked steady states. Using bifurcation and stability analysis, I will characterise the onset of pattern formation and identify parameter regimes in which these solutions exist and remain robust. This mechanism provides a mathematically distinct route to effective long-range inhibition, in contrast to curvature-morphogen coupling or classical Turing-type diffusion-driven instabilities. Model predictions are in quantitative agreement with experimental observations, suggesting that mechanically mediated feedback may constitute a fundamental organising principle in epithelial pattern formation.

10:30 – 11:20   Kousuke Kuto (Waseda University)

Abstract: This talk concerns asymptotic regimes of positive steady states in the Shigesada-Kawasaki-Teramoto competition model under large cross-diffusion limits. We present a systematic classification of limiting regimes according to unilateral or full cross-diffusion limits, together with boundary conditions including Neumann and Dirichlet cases. We explain how these four settings lead to distinct limiting shadow systems and determine qualitative structures of coexistence states, such as segregation, extinction, or concentration profiles. This classification provides a unified framework that organizes previously known results and clarifies structural relations between different limiting procedures. This talk is based on joint work with Profs. Yaping Wu (Capital Normal University) and Toru Kan (Osaka Metropolitan University).

11:30 -- 12:00   Szymon Cygan (Heidelberg University & University of Wroclaw)

13:30 -- 14:20   Hirokazu Ninomiya (Meiji University)

Abstract: In 1986, Gage studied area-preserving curvature flows in a two-dimensional homogeneous medium and proved that an initially convex closed curve remains convex and converges to a circle as time approaches infinity. However, in many applications, such as cell motility and the motion of active matter, the medium is often inhomogeneous. In this talk, I will introduce the following area-preserving curvature flow in an inhomogeneous medium, which can be regarded as a natural extension of the curvature flow in a homogeneous medium. Through this extension, a closed curve numerically moves towards the higher medium by the flow. To show this fact, the case is considered in which the area enclosed by the closed curve is small. In this situation, it is shown that the dynamics of its center is approximated by a gradient flow determined by the distribution of the inhomogeneous medium and that its center moves toward the critical point of the inhomogeneous medium.

14:30 -- 15:20   Kentaro Fujie (Tohoku University)

Abstact: In seminal works by Keller and Segel, some mathematical model was introduced to describe aggregation phenomena and pattern formations induced by chemotaxis effect. In the mathematical analysis of large time behaviour of solutions to this model, its entropy structure plays an important role. In this talk, we focus on the entropy production (the time derivative of the entropy) of the Keller–Segel system and related parabolic equations. The time evolution of the entropy production is discussed and some application of this property is also given.

15:40 -- 16:30   Goro Akagi

16:40 -- 17:10   Rong Lei (Tohoku University)

Abstract: We investigate the homogenization of a phase-field model for two-phase flow in porous media, incorporating surface tension effects. The model is governed by the coupled Stokes–Cahn–Hilliard system with a logarithmic free energy, where the two fluids are separated by a diffuse interface of finite width. We first prove some uniform energy estimate. Then, by the method of two-scale convergence and unfolding theory, we derive the homogenized limit, which takes the form of a generalized Richards’ equation. This is joint work with Jun Masamune.

9:30 -- 10:20   Chiun-Chuan Chen (National Taiwan University)

Abstract: We investigate the propagation direction of bistable traveling waves in the two-species Lotka–Volterra competition–diffusion model under strong competition. From an ecological perspective, the sign of the wave speed is critical, as it dictates which species eventually prevails. We propose a mini-max characterization of the coefficients in the reaction terms when the wave speed is zero. Applying our characterization, some explicit conditions under which the speed sign can be determined are obtained. We also focus on a near-symmetric scenario where intrinsic growth rates and inter-specific competition coefficients are identical, leaving diffusion rates as the sole source of asymmetry. This framework is motivated by Girardin et al.’s conjecture, which proposes that the species with the higher diffusion rate gains a competitive advantage, directly dictating the wave speed's sign. In this talk, we explore the subtle regime where inter-specific competition weakens, approaching the strong-competition boundary.

10:30 -- 11:20   Yasuhito Miyamoto (University of Tokyo)

Abstract: We show in a rigorous way that a stable internal single-layer stationary solution is destabilized by the Hopf bifurcation as the time constant exceeds a certain critical value. Moreover, the exact critical value and the exact period of oscillatory solutions can be obtained. The exact period indicates that the oscillation is very slow, i.e., the period is of order O(e^{C/ε}) We also rigorously prove that Hopf bifurcations from multi-layer stationary solutions occur. In this case anti-phase horizontal oscillations of layers are shown by formal calculations. Numerical experiments show that the exact period agrees with the numerical period of a nearly periodic solution near the Hopf bifurcation point. Anti-phase (out of phase) horizontal oscillations of layers are numerically observed.

11:30 -- 12:00   Shun-Chieh Wang

13:30 -- 14:20   Lorenzo Cavallina (Tohoku University)

Abstract: In this talk, I will discuss an overdetermined problem arising in the shape optimization problem of maximizing the torsional rigidity of composite beams made of two distinct materials separated by an interface. I will focus on two-phase configurations for which this overdetermined problem admits a solution, and I will present several qualitative and geometric properties of such configurations. In particular, I will explain how the geometry of the interface affects the overall configuration's shape, and show when optimal configurations are radially symmetric and when they are not.

14:30 -- 15:20   Shinya Okabe (Tohoku University)

Abstract: The ideal functional is defined by the Dirichlet energy of the curvature of curves and originates from an elasticity problem posed by Jacob Bernoulli in 1694. In this talk, we consider the length-penalised ideal curve flow for planar closed curves. Although one might expect the functional to have a similar variational structure to that of the well-known elastic energy due to its origin, the ideal functional has a quite different structure. One of the main results of this talk is that the length-penalised ideal curve flow blows up in finite time under a suitable condition on the initial curves. Furthermore, there are infinitely many kinds of critical points of the ideal functional with length penalisation. We will state this precisely as a second main result of the talk. This talk is based on joint work with Glen Wheeler at the University of Wollongong.

15:40 -- 16:30   Kanako Suzuki (Ibaraki University)

Abstract: We study the effect of a basal production term on an activator–inhibitor type reaction–diffusion system. When the basal production is a positive constant, the system admits a unique positive constant steady state. Under an appropriate change of variables, another constant steady state induced by the basal production term emerges. We discuss the existence of traveling wave solutions connecting this new steady state and the positive constant steady state. This is a joint work with Izumi Takagi (Tohoku University).

TBA ( University)