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Ushijima Lab
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The lab studies the properties of solutions to partial differential equations and numerical methods for solving them.
AboutAbout the lab
Investigating the properties of solutions to equations through both theory and numerical computation
The Ushijima Lab studies the properties of solutions to nonlinear parabolic partial differential equations and numerical methods for solving them.
Many natural phenomena, such as heat conduction, melting ice, growing crystals, and wave propagation, are described by equations called partial differential equations.
The lab investigates the properties of solutions from the perspectives of both numerical analysis and theoretical analysis.
Because the lab studies partial differential equations that serve as mathematical models for living organisms, it is interested in applications to problems in biology.
Key terms
- Partial differential equation
- An equation that describes how natural phenomena change, such as heat conduction and crystal growth
- Nonlinear parabolic partial differential equation
- A nonlinear equation among parabolic equations, which describe change over time such as how heat spreads
- Numerical method
- A method for approximately finding the solution of an equation as numerical values using a computer
ResearchResearch themes
Among the partial differential equations that describe various natural phenomena, the lab works with a class called nonlinear parabolic partial differential equations. It studies the properties of their solutions as well as numerical methods for computing those solutions.
*Illustrative imageProperties of Solutions to Nonlinear Parabolic Equations
The lab studies the properties of solutions to a class of equations called nonlinear parabolic partial differential equations. Its research aim is to investigate them from the perspectives of both numerical analysis and theoretical analysis.
*Illustrative imageNumerical Methods for Partial Differential Equations
The lab studies methods for finding solutions of partial differential equations numerically. It deals with numerical methods for solutions of nonlinear parabolic partial differential equations.
MembersFaculty
- ProfessorTakeo Ushijima
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: “Diffraction of plane wave from plasmonic slit” Myxomatosis57 / CC BY 4.0 (cropped)
- Properties of Solutions to Nonlinear Parabolic Equations: “Reaction-difusion patterns” Gnomo4453 / CC BY-SA 4.0 (cropped)
- Numerical Methods for Partial Differential Equations: “Crouzeix-Raviart-Finite-Elemente-Lösung” Grawiuton / CC0 (cropped)
- Related lab (伊藤・呼子研究室): “Würfel” Dietmar Rabich / CC BY-SA 4.0 (cropped)
- Related lab (側島研究室): “Round Chladni plate with 4 circular nodes” Pieter Kuiper / Public domain (cropped)
- Related lab (松本
（和） 研究室): “Domain coloring z 02” Djiboun / CC BY-SA 4.0 (cropped) - Related lab (江崎研究室): “WienerSausage” R.e.b. / Public domain (cropped)
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