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Applied Analysis Lab
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A lab that analyzes mathematical models of phenomena using modern mathematics.
AboutAbout the lab
Analyzing mathematical models of phenomena with mathematics.
The Applied Analysis Lab studies mathematical models, which express phenomena seen in nature and society as equations, by analyzing them with mathematical methods.
Its subjects are wide-ranging, including chemical reactions, fluid motion, the behavior of quantum-mechanical particles, and the progression of malignant tumors.
On the theoretical side, the lab investigates the properties of the partial differential equations obtained as models of phenomena, using methods of modern mathematics such as the calculus of variations, dynamical systems theory, and blow-up analysis.
On the applied side, the lab examines the properties of the equations through numerical simulation and compares the results with actual phenomena to verify the validity of the models.
Key terms
- Partial differential equation
- An equation that involves rates of change with respect to multiple variables, and appears as a mathematical model describing phenomena
- Variational analysis
- A mathematical method, based on the calculus of variations built on functional analysis, for examining the structure and properties of solutions to equations
- Dynamical system
- A mathematical description of how a state changes over time, used to study the long-time behavior of solutions
ResearchResearch themes
The Applied Analysis Lab studies the mathematical aspects of the mathematical-science approach to phenomena from a broad perspective. It investigates mathematical models that arise in medicine and biology, environmental science, fluid phenomena, and quantum phenomena, using variational analysis and dynamical systems theory.
*Illustrative imageAnalysis of Mathematical Models of Phenomena
The lab works on the analysis of mathematical models that arise in medicine and biology, environmental science, fluid phenomena, and quantum phenomena.
*Illustrative imageVariational Analysis
The lab studies the structure and geometry of solutions to critical elliptic equations, inequalities in real analysis that arise in gauge theory and the associated variational problems, and asymptotic mean value theorems for nonlinear harmonic functions, among other topics.
*Illustrative imageDynamical Systems Theory
The lab studies the behavior of solutions to critical semilinear parabolic equations, and the asymptotic behavior of dynamical systems whose orbits are not compact, along with methods for analyzing them.
MembersFaculty
The members of the Applied Analysis Lab consist of faculty members and doctoral, master's, and undergraduate students.
- ProfessorMichinori Ishiwata
- Associate ProfessorMasato Hashizume
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: “PCBThermalSimulation” Harke / Public domain (cropped)
- Analysis of Mathematical Models of Phenomena: “Nk model hypercube” Aeioun / CC BY-SA 3.0 (cropped)
- Variational Analysis: “Horgan's minimal non-surface” Anders Sandberg / CC BY 4.0 (cropped)
- Dynamical Systems Theory: “Intermittent Lorenz Attractor - Chaoscope” Anders Sandberg from Oxford, UK / CC BY 2.0 (cropped)
- Related lab (Differential Equations Lab): “Controur Boxplots Fluid Simulation median, order statistics, and outliers” Sciinstitute / CC BY-SA 3.0 (cropped)
- Related lab (Kawahara Lab): “Artificial Neural Network with Chip” mikemacmarketing / original posted on flickr Liam Huang / clipped and posted on flickr / CC BY 2.0 (cropped)
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