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Mitake Lab
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AboutAbout the lab
Reading equations of change through the power of analysis.
Mitake Lab studies partial differential equations that describe the motion and change of things, from the standpoint of mathematical analysis.
At the center of its work are the theory of viscosity solutions, which can handle solutions that are not smooth, and Hamilton-Jacobi equations.
The lab also works on problems connected to physics and engineering, such as how solutions settle down as time passes (large-time behavior), optimal control, and crystal growth.
ResearchResearch themes
*Illustrative imageAveraging out fine patterns
Phenomena inside materials where fine patterns repeat can be described, when viewed from far away, by averaged properties. The lab treats this "homogenization" using Hamilton-Jacobi equations, a type of partial differential equation, and studies how fast solutions approach the averaged result.
*Illustrative imageFlows of surfaces moving under force
The lab studies "forced mean curvature flow," in which a surface that moves according to its curvature is also acted on by an external force. It mathematically investigates the growth rate of the surface of spirally growing crystals, the motion of surfaces with a prescribed boundary, and the phenomenon of a surface disappearing partway through its motion.
MembersFaculty
- Hiroyoshi Mitake
VoicesStudent voices
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Report an errorAbout the images
The top and research theme images are illustrative and were not taken at the lab. They are cropped from Wikimedia Commons images. Cropped CC BY-SA images are provided under the same CC BY-SA license as the original (version shown on each line).
- Top image: “Bubble on an ultrahydrophobic surface” Stevearscott / CC BY-SA 4.0 (cropped)
- Averaging out fine patterns: “AEDC team members mark completion of 16S honeycomb (8205388)” U.S. Air Force photo by Staff Sgt. Keith Thornburgh / Public domain (cropped)
- Flows of surfaces moving under force: “Pyrite Navajun Screw Growth” Miguel Calvo / CC BY 4.0 (cropped)
- Related lab (Kozono Lab): “A340 wake turbulence simulation” Deutsches Zentrum für Luft und Raumfahrt / CC BY 3.0 de (cropped)
- Related lab (Ogawa Lab): “Chladni plate 14” Exhibit made by Estes Objethos Atelier, photo by Rodrigo Tetsuo Argenton / CC BY-SA 4.0 (cropped)
- Related lab (Ikeda Lab): “Mathematisches-Gipsmodell.Fläche3.Ordnung - Kopie” Museopedia / CC BY-SA 4.0 (cropped)
- Related lab (Usuba Lab): “CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique” Jérémy Barande / CC BY-SA 3.0 (cropped)
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