Ronald J. DiPerna (11 February 1947 – 8 January 1989) was an American mathematician, who worked on nonlinear partial differential equations. Diperna ronald 1985

Ronald Diperna was born in

Somerville, Massachusetts Somerville ( ) is a city located directly to the northwest of Boston, and north of Cambridge, Massachusetts, Cambridge, in Middlesex County, Massachusetts, United States. As of the 2020 United States census, the city had a total population of 81, ...

in 1947, and did his undergraduate studies at

Tufts University Tufts University is a private research university in Medford and Somerville, Massachusetts, United States, with additional facilities in Boston and Grafton, as well as Talloires, France. Tufts also has several Doctor of Physical Therapy p ...

before being advised to attend graduate school by Professor George Leger. In 1972 DiPerna received from the

Courant Institute of Mathematical Sciences The Courant Institute of Mathematical Sciences (commonly known as Courant or CIMS) is the mathematics research school of New York University (NYU). Founded in 1935, it is named after Richard Courant, one of the founders of the Courant Institute ...

his Ph.D. under

James Glimm James Gilbert Glimm (born March 24, 1934) is an American mathematician, former president of the American Mathematical Society, and distinguished professor at Stony Brook University. He has made many contributions in the areas of pure and applied ...

with thesis ''Global solutions to a class of nonlinear hyperbolic systems''. He held academic positions at

Brown University Brown University is a Private university, private Ivy League research university in Providence, Rhode Island, United States. It is the List of colonial colleges, seventh-oldest institution of higher education in the US, founded in 1764 as the ' ...

, the

University of Michigan The University of Michigan (U-M, U of M, or Michigan) is a public university, public research university in Ann Arbor, Michigan, United States. Founded in 1817, it is the oldest institution of higher education in the state. The University of Mi ...

, the

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, and

Duke University Duke University is a Private university, private research university in Durham, North Carolina, United States. Founded by Methodists and Quakers in the present-day city of Trinity, North Carolina, Trinity in 1838, the school moved to Durham in 1 ...

, before he became in 1985 a professor at the

University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California), is a Public university, public Land-grant university, land-grant research university in Berkeley, California, United States. Founded in 1868 and named after t ...

. He died unexpectedly at age 41 shortly after the end of a sabbatical year as a visiting scholar at the

Institute for Advanced Study The Institute for Advanced Study (IAS) is an independent center for theoretical research and intellectual inquiry located in Princeton, New Jersey. It has served as the academic home of internationally preeminent scholars, including Albert Ein ...

.Obituary at the University of California, by Alexandre Chorin, Craig Evans, James Gilman, Andrew Majda
/ref> In the last part of his career he worked with

Pierre-Louis Lions Pierre-Louis Lions (; born 11 August 1956) is a French mathematician. He is known for a number of contributions to the fields of partial differential equations and the calculus of variations. He was a recipient of the 1994 Fields Medal and the 19 ...

on integro-differential equations in the kinetic theory of gases (

Cauchy problem A Cauchy problem in mathematics asks for the solution of a partial differential equation that satisfies certain conditions that are given on a hypersurface in the domain. A Cauchy problem can be an initial value problem or a boundary value problem ...

for

Boltzmann equation The Boltzmann equation or Boltzmann transport equation (BTE) describes the statistical behaviour of a thermodynamic system not in a state of equilibrium; it was devised by Ludwig Boltzmann in 1872.Encyclopaedia of Physics (2nd Edition), R. G ...

s) and the plasma physics generalization (

Vlasov equation In plasma physics, the Vlasov equation is a differential equation describing time evolution of the distribution function of collisionless plasma consisting of charged particles with long-range interaction, such as the Coulomb interaction. The e ...

). He also worked on singularities in compressible flow. DiPerna with Andrew Majda began in 1986 research on the question of the existence of solutions to the

Euler equations In mathematics and physics, many topics are eponym, named in honor of Swiss mathematician Leonhard Euler (1707–1783), who made many important discoveries and innovations. Many of these items named after Euler include their own unique function, e ...

in two dimensions with initial conditions that are found in the evolution of vortex sheets. DiPerna and Majda introduced the ''Concentration-Cancellation'' Method. DiPerna was a

Guggenheim Fellow Guggenheim Fellowships are grants that have been awarded annually since by the John Simon Guggenheim Memorial Foundation, endowed by the late Simon and Olga Hirsh Guggenheim. These awards are bestowed upon individuals who have demonstrated d ...

for the academic year 1984–1985 and a

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for the academic year 1978–1979. In 1986 he was an

invited speaker at the International Congress of Mathematicians An invitation system is a method of encouraging people to join an organization, such as a Club (organization), club or a website. In regular society, it refers to any system whereby new members are chosen; they cannot simply apply. In relation to w ...

in Berkeley 1986 and gave a talk ''Compactness of solutions to nonlinear PDEs''. He was married to Maria E. Schonbek, a professor of mathematics at the

University of California, Santa Cruz The University of California, Santa Cruz (UC Santa Cruz or UCSC) is a public university, public Land-grant university, land-grant research university in Santa Cruz, California, United States. It is one of the ten campuses in the University of C ...

and had a daughter. He died in

Princeton, New Jersey The Municipality of Princeton is a Borough (New Jersey), borough in Mercer County, New Jersey, United States. It was established on January 1, 2013, through the consolidation of the Borough of Princeton, New Jersey, Borough of Princeton and Pri ...

in 1989, and in his honor the University of California at Berkeley established the DiPerna Lectures in Applied Mathematics.

Selected publications

* * *''Uniqueness of solutions to hyperbolic conservation laws'', Indiana Univ. Math. J. 28 (1979), 137–188. * *''Convergence of the viscosity method for isentropic gas dynamics'', Comm. Math. Phys. 91 (1983), 1–30
Online
*
''Compensated Compactness and general systems of Conservation Laws'', Transactions AMS, 292, 1985, 383-420
*with Pierre-Louis Lions: *with Pierre-Louis Lions: *with Lions:

References

{{DEFAULTSORT:DiPerna, Ronald 1947 births 1989 deaths 20th-century American mathematicians Courant Institute of Mathematical Sciences alumni University of California, Berkeley faculty American fluid dynamicists Partial differential equation theorists Institute for Advanced Study visiting scholars People from Somerville, Massachusetts Mathematicians from Massachusetts