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Miyamoto Lab
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The lab studies the nature of solutions to nonlinear partial differential equations.
AboutAbout the lab
The existence, number, and shape of solutions to equations.
The Miyamoto Lab studies nonlinear partial differential equations of the types known as elliptic and parabolic.
These equations are known to describe a wide range of phenomena that appear in the natural sciences and the social sciences.
The lab aims to clarify basic properties of solutions, such as their existence and non-existence, as well as qualitative properties such as the number and shape of solutions and their Morse index.
The lab is interested in both general methods that use functional analysis and individual methods that make use of the specific characteristics of each equation.
Key terms
- Partial differential equation
- An equation that expresses the relationship between a function of several variables and its rates of change (partial derivatives)
- Parabolic
- A type of partial differential equation that describes phenomena that change over time, such as the spread of heat
- Functional analysis
- A field of mathematics that treats functions like points and studies a collection of functions as a single space
ResearchResearch themes
The lab's research field is nonlinear partial differential equations, and its theme is the structure of solutions to elliptic and parabolic nonlinear partial differential equations. It aims to clarify properties of solutions such as their existence, number, and shape.
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MembersFaculty
- ProfessorYasuhito MiyamotoPublications ↗
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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: “TuringPattern” Ex.ungue.leonem / Public domain (cropped)
- Structure of Solutions to Nonlinear Partial Differential Equations: “Stationaer poisson” FabianStassek / CC BY-SA 4.0 (cropped)
- Related lab (Takada Lab): “Kelvin-Helmholtz instability clouds” Brocken Inaglory / CC BY-SA 3.0 (cropped)
- Related lab (Iwaki Lab): “AiryAi Abs Surface” Inductiveload / Public domain (cropped)
- Related lab (Sakai Lab): “Modell der Weierstraßschen p-Funktion -Schilling, XIV, 7ab, 8 - 313, 314” Oliver Zauzig / CC BY-SA 3.0 (cropped)
- Related lab (Shimomura Lab): “Traveling wave” P.wormer / CC BY-SA 3.0 (cropped)
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