mathematics

Panagiotis E. Souganidis

Panagiotis E. Souganidis 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 Panagiotis E. Souganidis rather than just read about it. In short: Panagiotis E. Souganidis (Παναγιώτης E. Σουγανίδης) is an American mathematician, specializing in partial differential equations.

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Reference excerpt

Panagiotis E. Souganidis (Παναγιώτης E. Σουγανίδης) is an American mathematician, specializing in partial differential equations.

Biography Souganidis graduated in 1981 with B.A. from the National and Kapodistrian University of Athens. At the University of Wisconsin–Madison he graduated with M.A. in 1981 and Ph.D. in 1984 with thesis under the supervision of Michael G. Crandall. Souganidis was a postdoc in 1984–1985 at the University of Minnesota's Institute for Mathematics and its Applications and was at the Institute for Advanced Study in 1988 and 1990. After holding professorships at Brown University, the University of Wisconsin–Madison, and the University of Texas at Austin, he became in 2008 the Charles H. Swift Distinguished Service Professor in Mathematics at the University of Chicago. He has held visiting positions at academic institutions in Italy, Japan, Greece, France, the UK, and Sweden.

He works on non-linear partial differential equations, and stochastic analysis. The main parts of his work are qualitative properties of viscosity and entropy solutions, front propagation and asymptotic behavior of reaction diffusion equations and particle systems, stochastic homogenization, the theory of pathwise solutions for first and second order partial differential equations, including stochastic Hamilton-Jacobi equations and scalar conservation laws. Souganidis is the author or co-author of over 100 publications in refereed journals. His wife is Thaleia Zariphopoulou, a Greek-American mathematician and professor at the University of Texas at Austin.

Awards and honors 1989 — Sloan Research Fellow 1994 — Invited Speaker of the International Congress of Mathematicians 2003 — Highly Cited Researcher 2012 — Fellow of the American Mathematical Society (Class of 2013) 2015 — Fellow of the Society for Industrial and Applied Mathematics 2017 — Fellow of the American Association for the Advancement of Science 2019 — Invited Speaker of the International Congress on Industrial and Applied Mathematics 2026 — Invited Speaker of the AIMS conference in Athens, Greece.

Selected publications Evans, L. C.; Souganidis, P. E. (1984). "Differential Games and Representation Formulas for Solutions of Hamilton-Jacobi-Isaacs Equations". Indiana University Mathematics Journal. 33 (5): 773–797. doi:10.1512/iumj.1984.33.33040. JSTOR 45010271. Souganidis, Panagiotis E. (1985). "Approximation schemes for viscosity solutions of Hamilton-Jacobi equations". Journal of Differential Equations. 59 (1): 1–43. Bibcode:1985JDE....59....1S. doi:10.1016/0022-0396(85)90136-6. Lions, P.-L.; Souganidis, P. E. (1985). "Differential Games, Optimal Control and Directional Derivatives of Viscosity Solutions of Bellman's and Isaacs' Equations". SIAM Journal on Control and Optimization. 23 (4): 566–583. doi:10.1137/0323036. Bona, J. L.; Souganidis, P. E.; Strauss, W. A. (1987). "Stability and Instability of Solitary Waves of Korteweg-de Vries Type". Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 411 (1841): 395–412. Bibcode:1987RSPSA.411..395B. doi:10.1098/rspa.1987.0073. S2CID 120894859. Fleming, W. H.; Souganidis, P. E. (1989). "On the Existence of Value Functions of Two-Player, Zero-Sum Stochastic Differential Games". Indiana University Mathematics Journal. 38 (2): 293–314. doi:10.1512/iumj.1989.38.38015. JSTOR 24895386. Bona, J. L.; Souganidis, P. E.; Strauss, W. A. (1987). "Stability and Instability of Solitary Waves of Korteweg-de Vries Type". Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 411 (1841): 395–412. Bibcode:1987RSPSA.411..395B. doi:10.1098/rspa.1987.0073. S2CID 120894859. Barles, G.; Soner, H. M.; Souganidis, P. E. (1993). "Front Propagation and Phase Field Theory". SIAM Journal on Control and Optimization. 31 (2): 439–469. doi:10.1137/0331021. S2CID 39091910. Lions, Pierre-Louis; Perthame, Benoît; Souganidis, Panagiotis E. (1998). "Existence and stability of entropy solutions for the hyperbolic systems of isentropic gas dynamics in Eulerian and Lagrangian coordinates". Communications on Pure and Applied Mathematics. 49 (6): 599–638. doi:10.1002/(SICI)1097-0312(199606)49:6<599::AID-CPA2>3.0.CO;2-5. Barles, Guy; Souganidis, Panagiotis E. (1998). "A New Approach to Front Propagation Problems: Theory and Applications". Archive for Rational Mechanics and Analysis. 141 (3): 237–296. Bibcode:1998ArRMA.141..237B. doi:10.1007/s002050050077. S2CID 121972598. Lions, Pierre-Louis; Souganidis, Panagiotis E. (2003). "Correctors for the homogenization of Hamilton-Jacobi equations in the stationary ergodic setting". Communications on Pure and Applied Mathematics. 56 (10): 1501–1524. doi:10.1002/cpa.10101. S2CID 121828182.

References

External links International Centre for Theoretical Physics (ICTP) talks by Panagiotis Souganidis, 2018 "Phase-field models for motion by mean curvature - 1". YouTube. ICTP Mathematics. 11 June 2018. "Phase-field models for motion by mean curvature - 2". YouTube. ICTP Mathematics. 12 June 2018. "Phase-field models for motion by mean curvature - 3". YouTube. ICTP Mathematics. 12 June 2018. "Phase-field models for motion by mean curvature - 4". YouTube. ICTP Mathematics. 14 June 2018.

Worked examples

Example 1 — a first encounter with Panagiotis E. Souganidis

Start with the simplest possible case. Write down what Panagiotis E. Souganidis 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 Panagiotis E. Souganidis 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 Panagiotis E. Souganidis 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 Panagiotis E. Souganidis

In research: Panagiotis E. Souganidis 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 Panagiotis E. Souganidis 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: Panagiotis E. Souganidis is common in secondary-school and first-year university syllabi. It links to neighbouring topics 20th-century American mathematicians, 21st-century American mathematicians, American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Panagiotis E. Souganidis 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 Panagiotis E. Souganidis in simple terms?

Panagiotis E. Souganidis (Παναγιώτης E. Σουγανίδης) is an American mathematician, specializing in partial differential equations.

Why does Panagiotis E. Souganidis 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 Panagiotis E. Souganidis?

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 Panagiotis E. Souganidis.