mathematics

Hitoshi Ishii

Hitoshi Ishii is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Hitoshi Ishii rather than just read about it. In short: Hitoshi Ishii (石井仁司 Ishii Hitoshi, born on 12 October 1947), a Japanese mathematician, who is specialized in partial differential equations. He first studied physics and then mathematics at Waseda University with a master's degree in 1972 and a doctorate in 1975 with dissertation "偏微分方程式の初期値問題のLP可解性及び一意性" (translation: "Lp solvability and uniqueness of the initial value problem for partial differential equations").

Key takeaways

Hitoshi Ishii belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Hitoshi Ishii to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Hitoshi Ishii from memory before moving on to harder problems.

Reference excerpt

Hitoshi Ishii (石井仁司 Ishii Hitoshi, born on 12 October 1947), a Japanese mathematician, who is specialized in partial differential equations. He first studied physics and then mathematics at Waseda University with a master's degree in 1972 and a doctorate in 1975 with dissertation "偏微分方程式の初期値問題のLP可解性及び一意性" (translation: "Lp solvability and uniqueness of the initial value problem for partial differential equations"). He became an assistant professor at Chūō University in 1976 and in 1989 a full professor. In 1996, he became a professor at Tokyo Metropolitan University and in 2001, he became a professor at Waseda University. He studies nonlinear partial differential equations (PDEs) such as Hamilton–Jacobi equation, viscosity solutions of PDEs, optimal control theory, differential games, and evolution of surfaces. From 1987 to 1988, he was a visiting professor at Brown University, in 2011 at Collège de France, and in 2010 at University of Chicago. From 2011 to 2014 he was an adjunct professor at King Abdulaziz University. In 1994, He received the Autumn Prize from the Mathematical Society of Japan. In 2002, he was named to the Thomson ISI list of highly cited researchers in mathematics. He was an invited speaker with talk Asymptotic solutions for large time of Hamilton-Jacobi equations at the International Congress of Mathematicians in 2006 in Madrid. He was an invited speaker at the 7th International Congress on Industrial and Applied Mathematics (ICIAM) 2007 in Zurich. In 2012 he was elected a Fellow of the American Mathematical Society.

Selected publications with Michael G. Crandall and Pierre-Louis Lions: User’s guide to viscosity solutions of second order partial differential equations. Bulletin AMS, vol. 27, 1992, 1–67 doi:10.1090/S0273-0979-1992-00266-5 mit Pierre-Louis Lions: Viscosity solutions of fully nonlinear second-order elliptic partial differential equations. Journal of Differential Equations, vol. 83, 1990, 26–78 doi:10.1016/0022-0396(90)90068-2 On uniqueness and existence of viscosity solutions of fully nonlinear second order elliptic PDE's. Communications on Pure and Applied Mathematics, vol. 42, 1989, 15–45 doi:10.1002/cpa.3160420103 Perron’s method for Hamilton-Jacobi equations. Duke Math. J., vol. 55, 1987, 369–384 doi:10.1215/S0012-7094-87-05521-9

References

External links Homepage with CV

Worked examples

Example 1 — a first encounter with Hitoshi Ishii

Start with the simplest possible case. Write down what Hitoshi Ishii claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Hitoshi Ishii before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Hitoshi Ishii ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Hitoshi Ishii

In research: Hitoshi Ishii appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Hitoshi Ishii in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Hitoshi Ishii is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1947 births, 20th-century Japanese mathematicians, 21st-century Japanese mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Hitoshi Ishii outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Hitoshi Ishii in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Hitoshi Ishii means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Hitoshi Ishii out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Hitoshi Ishii in simple terms?

Why does Hitoshi Ishii matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Hitoshi Ishii?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Hitoshi Ishii.