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Analysis Lab (Erika Ushikoshi)
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The lab studies how small changes in a domain affect the solutions and eigenvalues of equations.
AboutAbout the lab
Exploring how slight changes in a domain affect solutions
Associate Professor Erika Ushikoshi specializes in the theory of partial differential equations, within the field of analysis.
Partial differential equations describe natural phenomena mathematically on the basis of physical laws, and the lab aims to understand the essence of these phenomena more deeply through their analysis.
In particular, the lab mathematically examines how the solutions and eigenvalues of equations are affected when a small perturbation is applied to the domain.
The equations studied are the Navier–Stokes equations, the Stokes equations (their linearization), and the Lamé equations, which describe the vibration of elastic bodies.
Key terms
- Partial differential equation
- A mathematical expression that describes a natural phenomenon on the basis of physical laws.
- Domain perturbation
- Applying a small change to the domain on which an equation is considered.
- Navier–Stokes equations
- Equations known as the fundamental equations of fluid dynamics.
- Lamé equations
- Equations that describe the vibration of elastic bodies.
ResearchResearch themes
The lab analyzes natural phenomena mathematically through partial differential equations, aiming to understand the essence of these phenomena more deeply. It investigates how the solutions and eigenvalues of equations are affected when a small perturbation is applied to the domain.
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MembersFaculty
- Associate ProfessorErika Ushikoshi
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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: “Partial Differential Equations” Bernard Epstein / Public domain (cropped)
- Effects of Domain Perturbation on Solutions: “KirchhoffPlate” Luděk Sosnovec / CC BY-SA 4.0 (cropped)
- Related lab (Partial Differential Equations Lab (Tomoyuki Tanaka)): “Soliton 2nd order” Alessio Damato / CC BY-SA 3.0 (cropped)
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