PDE theorists

Charles Edmond Alfred Riquier (19 November 1853, Amiens – 17 January 1929, Caen) was a French mathematician.Riquier matriculated in 1873 at the École Normale Supérieure (ENS) where he received his agrégé in mathematics in 1876. He taught from 1876 to 1878 at the Lycée de Brest and then from 1878 to 1886 at the Lycée de Caen and from 1886 to 1924 at the Université de Caen, where he retired as a professor emeritus.
After a brief leave of absence from the Lycée de Caen, Riquier received his doctorate in mathematics in 1886 from ENS at Paris with dissertation Extension à l’hyperespace de la méthode de M. Carl Neumann pour la résolution de problèmes relatifs aux fonctions de variables réelles à laplacien nul. His thesis committee consisted of Hermite (as chair), Darboux, and Picard.In 1910 he was awarded the Poncelet Prize. In 1920 he was elected to the French Academy of Sciences as the successor to Hieronymus Zeuthen. (Eugène Fabry was elected Riquier's successor in 1931.)
Riquier, Maurice Janet, Joseph Miller Thomas, Joseph Fels Ritt, and Ellis Kolchin were among the greatest pioneers of differential algebra and symbolic computation for systems of partial differential equations.

Oskar Perron (7 May 1880 – 22 February 1975) was a German mathematician.
He was a professor at the University of Heidelberg from 1914 to 1922 and at the University of Munich from 1922 to 1951. He made numerous contributions to differential equations and partial differential equations, including the Perron method to solve the Dirichlet problem for elliptic partial differential equations. He wrote an encyclopedic book on continued fractions Die Lehre von den Kettenbrüchen. He introduced Perron's paradox to illustrate the danger of assuming that the solution of an optimization problem exists:

Let N be the largest positive integer. If N > 1, then N2 > N, contradicting the definition of N. Hence N = 1.

Henri Berestycki (born 25 March 1951) is a French mathematician who obtained his PhD from Université Paris VI – Pierre and Marie Curie University in 1975. His Dissertation was titled Contributions à l'étude des problèmes elliptiques non linéaires, and his doctoral advisor was Haïm Brezis. He was an L.E. Dickson Instructor in Mathematics at the University of Chicago from 1975–77, after which he returned to France to continue his research. He has made many contributions in nonlinear analysis, ranging from nonlinear elliptic equations, hamiltonian systems, spectral theory of elliptic operators, and with applications to the description of mathematical modelling of fluid mechanics and combustion. His current research interests include the mathematical modelling of financial markets, mathematical models in biology and especially in ecology, and modelling in social sciences (in particular, urban planning and criminology). For these latter topics, he obtained an ERC Advanced grant in 2012.
He worked at the French National Center of Scientific Research (CNRS), then moved to an appointment as Professor at University Paris XIII (1983–1985). He became a Professor of Mathematics in 1988 at Université Pierre et Marie Curie, Paris VI (1988–2001 of “exceptional class” since 1993), and became professor at École normale supérieure, Paris (1994–1999), and part-time professor at the École Polytechnique (1987–1999). He is also a visiting Professor in the Department of Mathematics at the University of Chicago, and was also co-director of the Stevanovich Center of Financial Mathematics in Chicago. He is currently the Directeur d'études (Research Professor) at École des hautes études en sciences sociales (EHESS), since 2001.

Yvonne Choquet-Bruhat (French: [ivɔn ʃɔkɛ bʁy.a] ; born 29 December 1923) is a French mathematician and physicist. She has made seminal contributions to the study of Einstein's general theory of relativity, by showing that the Einstein equations can be put into the form of an initial value problem which is well-posed. In 2015, her breakthrough paper was listed by the journal Classical and Quantum Gravity as one of thirteen 'milestone' results in the study of general relativity, across the hundred years in which it had been studied.She was the first woman to be elected to the French Academy of Sciences and is a Grand Officier of the Légion d'honneur.