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Tanaka Lab
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An analysis lab that uses the calculus of variations to show the existence of solutions to differential equations.
AboutAbout the lab
Finding solutions to differential equations through the calculus of variations.
Tanaka Lab uses the calculus of variations to show that solutions to differential equations exist.
Variational problems appear in many places: Fermat's principle (light travels along the shortest path) and the Dirichlet principle, both known as variational principles, as well as geodesics and brachistochrones.
Such problems can be solved by finding the function that attains the minimum of a real-valued function whose domain is a set of functions (a functional).
The lab examines the extrema of functionals to show the existence of solutions to differential equations.
Key terms
- Functional
- A real-valued function whose domain is a set of functions. Finding the function that attains its minimum solves a variational problem.
- Variational principle
- Examples include Fermat's principle (light travels along the shortest path) and the Dirichlet principle.
NewsLab news
View More ↗ResearchResearch themes
The lab examines the extrema of functionals to show the existence of solutions to differential equations. Its field of specialization is analysis, and its research field is the calculus of variations.
*Illustrative imageFinding solutions to differential equations through the calculus of variations
The lab examines the extrema of functionals to show that solutions to differential equations exist. Because the shape of a functional's graph is important, topological methods are also a related research area.
*Illustrative imageEigenvalue problems for elliptic operators
The lab studies eigenvalue problems for quasilinear elliptic operators, centering on variational methods. It also works on problems related to the eigenvalue problem for the p-Laplacian.
MembersFaculty
- Associate ProfessorMieko Tanaka
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: “Frostedbubble2” Daniela Rapavá / CC BY-SA 4.0 (cropped)
- Finding solutions to differential equations through the calculus of variations: “Soap film 3” Umberto Salvagnin / CC BY 2.0 (cropped)
- Eigenvalue problems for elliptic operators: “Sand Art” Aliva Sahoo / CC BY-SA 4.0 (cropped)
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