mathematics

Juan Luis Vázquez Suárez

Juan Luis Vázquez Suárez 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 Juan Luis Vázquez Suárez rather than just read about it. In short: Juan Luis Vázquez Suárez is a professor of Applied Mathematics at Universidad Autónoma de Madrid (UAM), Spain. Education He was born in Oviedo on July 26, 1946.

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Reference excerpt

Juan Luis Vázquez Suárez is a professor of Applied Mathematics at Universidad Autónoma de Madrid (UAM), Spain.

Education He was born in Oviedo on July 26, 1946. In the years 1964/69 he studied Telecommunication Engineering at the Superior Technical School of Ingenieros de Telecomunicación (ETSIT) in Madrid. In 1973 he graduated in Mathematics at the Universidad Complutense de Madrid, where he also obtained the Ph. D. degree in 1979 with a thesis directed by Haïm Brezis and Jesús Ildefonso Díaz.

Contributions His research covers areas of mathematics such as nonlinear partial differential equations and their applications to physics and engineering. He published in scientific journals like Archive for Rational Mechanics and Analysis, Communications on Pure and Applied Mathematics, Journal de mathématiques pures et appliquées, Advances in Mathematics among others. He was president of Spanish Society for Applied Mathematics in the period 1996/98. Organizer of international events like the International Conference on Free Boundaries FB1993 (Toledo, Spain) or the Summer Schools at the Universidad Internacional Menéndez Pelayo, UIMP.

Awards and honors He obtained the Spanish National Prize of Research in Mathematics in 2003, and that year he was included in the Thomson Reuters list of Highly Cited Scientists. He was invited as main speaker at the International Congress of Mathematicians held in Madrid in 2006 (ICM2006) with the plenary conference entitled "Nonlinear diffusion, from analysis to physics and geometry." In 2012 he became a fellow of the American Mathematical Society.

Journal articles Bonforte, M.; Dolbeault, J.; Grillo, G.; Vázquez, J. L. (September 7, 2010). "Sharp rates of decay of solutions to the nonlinear fast diffusion equation via functional inequalities". Proceedings of the National Academy of Sciences of the United States of America. 107 (38): 16459–16464. doi:10.1073/pnas.1003972107. PMC 2944723. Zbl 1256.35026. Caffarelli, Luis; Vazquez, Juan Luis (2011). "Nonlinear Porous Medium Flow with Fractional Potential Pressure". Archive for Rational Mechanics and Analysis. 202: 537–565. arXiv:1001.0410. doi:10.1007/s00205-011-0420-4. de Pablo, Arturo; Quirós, Fernando; Rodríguez, Ana; Vázquez, Juan Luis (2011). "A fractional porous medium equation". Advances in Mathematics. 226 (2): 1378–1409. doi:10.1016/j.aim.2010.07.017. Zbl 1208.26016. de Pablo, Arturo; Quirós, Fernando; Rodríguez, Ana; Vázquez, Juan Luis (2012). "A general fractional porous medium equation". Communications on Pure and Applied Mathematics. 65 (9): 1242–1284. doi:10.1002/cpa.21408. Zbl 1248.35220. Bonforte, Matteo; Grillo, Gabriele; Vázquez, Juan Luis (2012). "Behaviour near extinction for the fast diffusion equation on bounded domains". Journal de Mathématiques Pures et Appliquées. 97 (1): 1–38. doi:10.1016/j.matpur.2011.03.002. Zbl 1241.35013. Caffarelli, Luis; Soria, Fernando; Vázquez, Juan Luis. "Regularity of solutions of the fractional porous medium flow". Journal of the European Mathematical Society. 15 (5): 1701–1746. doi:10.4171/JEMS/401.

Books The Porous Medium Equation. Mathematical Theory. Oxford University Press, ISBN 0-19-856903-3, ISBN 978-0-19-856903-9, 2006, Clarendon Press, 648 pages, 234x156 mm. Series: Oxford Mathematical Monographs. Smoothing and Decay Estimates for Nonlinear Diffusion Equations. Equations of Porous Medium Type. Oxford University Press, ISBN 0-19-920297-4, ISBN 978-0-19-920297-3, August 2006, 248 pages, 234x156 mm, Oxford Lecture Series. A Stability Technique for Evolution Partial Differential Equations. A Dynamical Systems Approach. PNLDE 56 (Progress in Non-Linear Differential Equations and Their Applications), Birkhäuser Verlag, 2003, 391 pages. (with V.A. Galaktionov.) Recent Trends in Partial Differential Equations. American Mathematical Society, ISBN 0-8218-3891-1 ISBN 978-0-8218-3891-4, 2006, 123 pages, Series: Contemporary Mathematics number 409; (with X. Cabré and José A. Carrillo)

References

External links Official Web Page Departamento de Matemáticas UAM

Worked examples

Example 1 — a first encounter with Juan Luis Vázquez Suárez

Start with the simplest possible case. Write down what Juan Luis Vázquez Suárez 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 Juan Luis Vázquez Suárez 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 Juan Luis Vázquez Suárez 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 Juan Luis Vázquez Suárez

In research: Juan Luis Vázquez Suárez 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 Juan Luis Vázquez Suárez 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: Juan Luis Vázquez Suárez is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1946 births, 20th-century Spanish mathematicians, 21st-century Spanish mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Juan Luis Vázquez Suárez 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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Frequently asked questions

What is Juan Luis Vázquez Suárez in simple terms?

Juan Luis Vázquez Suárez is a professor of Applied Mathematics at Universidad Autónoma de Madrid (UAM), Spain. Education He was born in Oviedo on July 26, 1946.

Why does Juan Luis Vázquez Suárez 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 Juan Luis Vázquez Suárez?

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 Juan Luis Vázquez Suárez.