LAB LOGA page on LabLog, a review site (not the lab's official page)
Koike Lab
Machine-translated · View original
A lab that studies the smoothness of solutions to equations using the theory of viscosity solutions.
AboutAbout the lab
From nonlinear to fully nonlinear.
The Koike Lab studies, from a mathematical standpoint, the partial differential equations that describe natural phenomena and engineering problems.
In many cases the solutions cannot be written as explicit formulas, so the lab first finds a "solution in a weak sense" and then shows that it is a true solution.
Equations that arise in engineering and optimal control are called fully nonlinear, and a type of weak solution called a viscosity solution is used for this class.
The current focus is regularity theory, which investigates how smooth those viscosity solutions are.
Key terms
- Partial differential equation
- An equation expressing relationships among quantities obtained by differentiating with respect to several variables. It is used to describe natural phenomena.
- Viscosity solution
- A weak solution devised for equations to which integration by parts cannot be applied. It is derived from the maximum principle.
- Regularity theory
- A theory that examines how smooth a weak solution is and to what extent it can be regarded as a true solution.
ResearchResearch themes
Many phenomena in physics, biology, and chemistry are written as partial differential equations, which are studied as a major field of mathematics. This lab studies the properties of solutions to fully nonlinear equations, which are not amenable to integration by parts, through the notion of viscosity solutions.
*Illustrative imageFully Nonlinear Equations and Viscosity Solutions
Equations expressed through the dynamic programming principle, as in engineering and optimal control theory, are not suited to integration by parts. The lab works on viscosity solutions, introduced in the early 1980s for such equations, from both theoretical and applied perspectives.
*Illustrative imageRegularity Theory of Viscosity Solutions
The study of partial differential equations divides into a first half, finding a solution in a weak sense, and a second half, showing that it is a true solution. Regularity theory, which corresponds to the second half, is the current focus of the lab's research.
*Illustrative imageExpanding Applications of Viscosity Solutions
The idea of viscosity solutions has found applications in optimal control, differential games, curvature flow equations, phase transition problems, mathematical finance, and image processing. In recent years the lab has also turned its attention to applications to mean field games.
MembersFaculty
- ProfessorShigeaki Koike
VoicesStudent voices
Ratings and reviews reflect the experiences of individual current or former students, not the lab's official views. Whether a lab has reviews, or how many, says nothing about the lab itself.
Students who take part in an interview may receive a thank-you gift worth ¥1,000, regardless of what they say.
Student ratings (0 students)
--
--
--
--
--
--
Student voices answer questions like these
- What's great about this lab?
- What did you learn after joining?
- What's the vibe, and what is the professor like?
- Who is this lab for?
- Where do graduates go?
Your experience can help younger students choose their lab. Your name won't be shown.
Write a lab reviewAnonymous · Your draft is saved if you stopRelatedLabs similar to Koike Lab
Harayama LabSchool of Advanced Science and Engineering, Department of Applied PhysicsNonlinear physics
Aoki LabSchool of Advanced Science and Engineering, Department of Applied PhysicsQuantum optics
Ozawa LabSchool of Advanced Science and Engineering, Department of Applied PhysicsMathematical Physics
Kataoka LabSchool of Advanced Science and Engineering, Department of Applied PhysicsHigh-energy astrophysics and medical applicationsThe information on this page is compiled by the LabLog team from the lab's public information and interviews. For corrections or removal requests, please contact LabLog, not the lab.
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: “Minimal surface” Daniela_deGol / CC BY 4.0 (cropped)
- Fully Nonlinear Equations and Viscosity Solutions: “Modell einer Minimalfläche mit einer einparametrigen Familie von Parabeln -Schilling XVII, 1 - 248” Oliver Zauzig / CC BY-SA 3.0 (cropped)
- Regularity Theory of Viscosity Solutions: “Modelle von Flächen zweiter Ordnung nach A. Brill -Schilling, Cartonmodelle” Ramona Trusheim / CC BY-SA 3.0 (cropped)
- Expanding Applications of Viscosity Solutions: “Apus apus flock flying” Keta / CC BY-SA 2.5 (cropped)
- Related lab (原山研究室): “Neighborhood of attractor of discretized Lorenz system. XYZ(9) plane” German A. Chernykh & Irina A. Chernykh / CC BY-SA 4.0 (cropped)
- Related lab (
青木研究室): “Fibres optique” Pastèque24 / CC BY-SA 4.0 (cropped) - Related lab (小澤研究室): “World First Hiperboloid structure named Shukhov Tower in Polibino” Arssenev / CC BY-SA 4.0 (cropped)
- Related lab (片岡研究室): “Fermi Gamma-ray Space Telescope spacecraft model” NASA / Public domain (cropped)
About LabLog
LabLog is a lab review app for students only. Student members at each university interview students in labs and publish what they say. Student voices can only be read by students who sign up with a university email address. Operated by bestiee Inc.
Learn more about LabLog ↗Search engines and AI may reference the basic lab info and rating summaries on this page and the description of LabLog. Student voices are for student members only. Automated collection by programs (scraping, or input to or training of AI) is prohibited under Article 8 of the Terms of Service. If you need data for research or analysis, please contact us.