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Fourier Analysis and Partial Differential Equations Lab
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The lab uses harmonic analysis to study solutions to equations that describe wave phenomena.
AboutAbout the lab
Studying wave equations through harmonic analysis
Prof. Kinoshita studies the theory of partial differential equations and harmonic analysis.
The focus is on dispersive and wave equations, which describe a wide range of wave phenomena arising in quantum mechanics, plasma engineering, and fluid dynamics.
Given information at a certain time (the initial data), the research shows that a solution exists and is unique, and then examines how that solution behaves.
Harmonic analysis, especially Fourier restriction theory, plays a major role as a tool for this.
Key terms
- Partial differential equation
- An equation that describes how a quantity determined by several variables, such as time and position, changes
- Dispersive
- A property whereby the speed of a wave depends on its wavelength, so that waves spread out over time
- Harmonic analysis
- A branch of analysis that decomposes a function into wave components at each frequency and studies their magnitudes and properties
ResearchResearch themes
The lab studies nonlinear dispersive and wave equations that describe wave phenomena arising in quantum mechanics, plasma engineering, and fluid dynamics. The aim is to prove the existence and uniqueness of solutions and to examine the behavior of the solutions obtained.
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MembersFaculty
- Associate ProfessorShinya Kinoshita
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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: “Unusual wave at the Gap” Avenue / CC BY-SA 3.0 (cropped)
- Dispersive and Wave Equations and Harmonic Analysis: “Ripple-tank-parabolic-mirror” MikeRun / CC BY-SA 4.0 (cropped)
- Related lab (Fourier Analysis and Partial Differential Equations Lab): “Ocean waves water” Jon Sullivan / Public domain (cropped)
- Related lab (Fourier Analysis and Partial Differential Equations Lab): “Ashbridge's Bay ripples, July 2019” Jason Zhang / CC BY-SA 3.0 (cropped)
- Related lab (Hishida Lab): “F1 CFD Simulation” Cofaser / CC BY-SA 4.0 (cropped)
- Related lab (Fourier Analysis, Partial Differential Equations, and Fluid Dynamics Lab): “Flow separation” Jaganath at English Wikipedia / CC BY-SA 3.0 (cropped)
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