Ronald DiPerna

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Ronald J. DiPerna (born February 11, 1947 in Somerville (Massachusetts) , † January 8, 1989 in Princeton ) was an American mathematician who dealt with nonlinear partial differential equations (PDE). He was a professor at the University of California, Berkeley .

Ronald DiPerna, Berkeley 1985

life and work

DiPerna received his doctorate in 1972 under James Glimm at the Courant Institute of Mathematical Sciences of New York University ( Global solutions to a class of nonlinear hyperbolic systems ). He then went to Brown University , the University of Michigan , the University of Wisconsin and Duke University before joining Berkeley as a professor in 1985. He died at the age of only 41 while he was a visiting scholar at the Institute for Advanced Study .

He dealt with nonlinear PDE in particular from hydrodynamics and kinetic gas theory. There he developed the method of compensated compactness . He thus proved the global existence of weak solutions in equations of gas dynamics, and obtained results on the uniqueness, regularity and the asymptotic behavior of solutions. Most recently he dealt with integro-differential equations of kinetic gas theory ( Boltzmann equation and its plasma physics variant, the Vlasov equation), in collaboration with Pierre-Louis Lions , and singularities in incompressible flow. From 1986 with Andrew Majda he began studying Euler's equations in two dimensions with vortices as initial conditions and the question of the existence of global solutions in time (introduction of the concentration cancellation method).

He was a Guggenheim Fellow and a Sloan Research Fellow . He was invited speaker at the International Congress of Mathematicians in Berkeley in 1986 ( Compactness of solutions to nonlinear PDE ).

He was married to Maria Schonbeck, Professor of Mathematics at the University of California, Santa Cruz , and had one daughter.

DiPerna Lectures

The annual DiPerna Lectures in Applied Mathematics, which were first held in 1991, are named in his honor in Berkeley.

Fonts

  • Global solutions to a class of nonlinear hyperbolic systems of equations , Comm. Pure Appl. Math. 26: 1-28 (1973)
  • Existence in the large for quasilinear hyperbolic conservation laws , Arch. Rational Mech. Anal. 52: 244-257 (1973)
  • Uniqueness of solutions to hyperbolic conservation laws , Indiana Univ. Math. J. 28: 137-188 (1979).
  • Convergence of approximate solutions to conservation laws , Arch. Rational Mech. Anal. 1983, 82: 27-70.
  • Convergence of the viscosity method for isentropic gas dynamics , Comm. Math. Phys. 1983, 91: 1-30, online
  • Measure-valued solutions to conservation laws , Arch. Rational Mech. Anal. 1985, 88: 223-270.
  • Compensated Compactness and general systems of Conservation Laws , Transactions AMS, 292, 1985, 383-420
  • with Pierre-Louis Lions Global weak solutions of Vlasov-Maxwell systems , Comm. Pure Applied Math., 42, 1989, 729-757
  • with Pierre-Louis Lions On the Cauchy problem for Boltzmann equations: global existence and weak stability , Annals of Mathematics, 130, 1989, 321–366
  • with Lions: Ordinary differential equations, Sobolev spaces and transport theory , Inventiones Mathematicae, 98, 1989, 511-547

Web links

Individual evidence

  1. ↑ Ronald DiPerna in the Mathematics Genealogy Project (English)Template: MathGenealogyProject / Maintenance / id used
  2. ↑ DiPerna, Majda Concentrations in regularizations for 2-D incompressible flow , Comm. Pure Appl. Math. 40 (1987), 301-345, DiPerna, Majda Reduced Hausdorff dimension and concentration-cancellation for two-dimensional incompressible flow , J. Amer. Math. Soc. 1: 59-95 (1988).
  3. ^ DiPerna Lectures
personal data
SURNAME DiPerna, Ronald
ALTERNATIVE NAMES DiPerna, Ronald J.
BRIEF DESCRIPTION American mathematician
DATE OF BIRTH February 11, 1947
PLACE OF BIRTH Somerville, Massachusetts
DATE OF DEATH January 8, 1989
Place of death Princeton