Publications

2025

• K. Furukawa,
  “Well-Posedness of the Cauchy Problem for One-Dimensional Nonlinear Diffusion Equations with Dynamic and Fourth-Type Boundary Conditions in the \( Lp \) \( Lq \) Maximal Regularity Setting”, arXiv preprint, 2025.8.

• K. Furukawa,
  “Data assimilation for the primitive equations in \( H^2 \)”, Nonlinearity, 38, 7, Paper No. 075020, 2025.6.

• K. Furukawa, Y. Giga, N. Kajiwara,
  “No formation of a new phase for a free boundary problem in combustion theory”, Journal of Elliptic and Parabolic Equations, 2025.6.

• K. Furukawa, Y. Giga, M. Hieber, A. Hussein, T. Kashiwabara, M. Wrona,
  “The three limits of the hydrostatic approximation”, J. Lond. Math. Soc., 111, 4, 2025.4.

2024

• K. Furukawa,
  “Data Assimilation to the Primitive Equations with \( L^p \)-\( L^q \)-based Maximal Regularity Approach”, J. Math. Fluid Mech., 26, no. 9, 1-32, 2024.12.

• K. Furukawa, H. Kitahata,
  “Modeling and mathematical analysis of the clogging phenomenon in filtration filters installed in aquaria”, Partial Differ. Equ. Appl., 6, 1, 2024.1.

• K. Furukawa, H. Sakamoto, O. Marimo, S. Shima, T. Sulka, T. Miyoshi,
  “Particle filter data assimilation for ubiquitous unstable trajectories of two-dimensional three-state cellular automata”, Nonlinear Dyn., 2024.1.

2022

• K. Furukawa and T. Kashiwabara,
  “JUSTIFICATION OF THE HYDROSTATIC APPROXIMATION OF THE PRIMITIVE EQUATIONS IN ANISOTROPIC SPACE \( L^{\infty}H L^q{x_3}(\mathbb{T}^3) \)”, Advances in Mathematical Sciences and Applications, no. 1, 45-71, 2022.11.

2021

• K. Furukawa and N. Kajiwara,
  “Maximal \( L_p \)-\( L_q \) regularity for the quasi-steady elliptic problems”, J. Evol. Equ., 21, no. 2, 1601-1625, 2021. 12.

• K. Furukawa, Y. Giga, and T. Kashiwabara,
  “The hydrostatic approximation for the primitive equations by the scaled Navier-Stokes equations under the no-slip boundary condition”, J. Evol. Equ. 21, no. 3, 3331-3373, 2021.9.

2020

• K. Furukawa, Y. Giga, M. Hieber, A. Hussein, T. Kashiwabara, and M. Wrona,
  “Rigorous justification of the hydrostatic approximation for the primitive equations by scaled Navier-Stokes equations”, Nonlinearity 33, no. 12, 6502-6516, May 2020, DOI 10.1088/1361-6544/aba509.

• K. Furukawa,
  “Asymptotic Stability of Small Oseen Type Vortex under Three-Dimensional Large Perturbation”, Analysis (Berlin), no. 2, 57-83, Mar. 2020.