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Analysis 1 (Theory of Partial Differential Equations, Mean Curvature Flow) Lab (Keisuke Takasao)
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The lab studies mean curvature flow, which describes the motion of surfaces.
AboutAbout the lab
Tracking the shape of moving surfaces with equations.
The Takasao Lab studies nonlinear partial differential equations in the field of analysis.
Its main research subject is the mean curvature flow equation, which describes surfaces that move according to how much they curve.
In collaborative research, the lab also works on equations tied to real phenomena, such as the motion of grain boundaries in crystals and models of self-propelled objects.
Key terms
- Mean curvature flow
- A flow in which each point of a surface moves at a speed determined by the curvature (mean curvature) at that point
- Weak solution
- A solution that satisfies an equation in a sense with weaker smoothness requirements, so it can be handled even when singularities appear
- Allen-Cahn equation
- An equation describing the motion of the boundary between two states. In the limit where the boundary becomes thin, it approaches mean curvature flow
ResearchResearch themes
The lab studies the theory of nonlinear partial differential equations, in particular the mean curvature flow equation.
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MembersFaculty
- Associate ProfessorKeisuke Takasao
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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: “Reflection in a soap bubble edit” Brocken Inaglory. The image was edited by user:Alvesgaspar / CC BY-SA 3.0 (cropped)
- Volume-preserving mean curvature flow: “Costa minimal surface” en:User:Metlin / CC BY 2.5 (cropped)
- Related lab (Analysis 1 (Partial Differential Equations, Geometric Analysis, Calculus of Variations) Lab (Tatsuya Miura)): “Elastica-ExperimentalCurveShapesAndForces” Klemen Cotic / CC BY-SA 3.0 (cropped)
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