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<title>Ronald DiPerna</title>

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<h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Ronald DiPerna</span></h1>

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<div id="mw-content-text" class="mw-body-content mw-content-ltr" lang="de" dir="ltr"><div class="mw-content-ltr mw-parser-output" lang="de" dir="ltr"><p><b>Ronald J. DiPerna</b> (* <a href="11._Februar" title="11. Februar">11. Februar</a> <a href="1947" title="1947">1947</a> in <a href="Somerville_(Massachusetts)" title="Somerville (Massachusetts)">Somerville</a>, <a href="Massachusetts" title="Massachusetts">Massachusetts</a>; † <a href="8._Januar" title="8. Januar">8. Januar</a> <a href="1989" title="1989">1989</a> in <a href="Princeton_(New_Jersey)" title="Princeton (New Jersey)">Princeton</a>, <a href="New_Jersey" title="New Jersey">New Jersey</a>) war ein <a href="Vereinigte_Staaten" title="Vereinigte Staaten">US-amerikanischer</a> <a href="Mathematiker" title="Mathematiker">Mathematiker</a>, der sich mit nichtlinearen <a href="Partielle_Differentialgleichung" title="Partielle Differentialgleichung">Partiellen Differentialgleichungen</a> (PDE) befasste. Er war Professor an der <a href="University_of_California%2C_Berkeley" title="University of California, Berkeley">University of California, Berkeley</a>.

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<div class="mw-heading mw-heading2"><h2 id="Leben_und_Werk">Leben und Werk</h2></div>

<p>DiPerna wurde 1972 bei <a href="James_Glimm" title="James Glimm">James Glimm</a> am <a href="Courant_Institute_of_Mathematical_Sciences_of_New_York_University" title="Courant Institute of Mathematical Sciences of New York University">Courant Institute of Mathematical Sciences of New York University</a> <a href="Promotion_(Doktor)" title="Promotion (Doktor)">promoviert</a> (<i>Global solutions to a class of nonlinear hyperbolic systems</i>).<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> Danach war er an der <a href="Brown_University" title="Brown University">Brown University</a>, der <a href="University_of_Michigan" title="University of Michigan">University of Michigan</a>, der <a href="University_of_Wisconsin" class="mw-redirect" title="University of Wisconsin">University of Wisconsin</a> und der <a href="Duke_University" title="Duke University">Duke University</a>, bevor er 1985 als Professor nach Berkeley kam. Er starb mit nur 41 Jahren als er gerade Gastwissenschaftler am <a href="Institute_for_Advanced_Study" title="Institute for Advanced Study">Institute for Advanced Study</a> war.

</p><p>Er befasste sich mit nichtlinearen PDE insbesondere aus Hydrodynamik und kinetischer Gastheorie. Dort entwickelte er die Methode der <i>kompensierten Kompaktheit</i> (Compensated Compactness). Damit bewies er die globale Existenz von schwachen Lösungen bei Gleichungen der Gasdynamik, erzielte Resultate über die Eindeutigkeit, Regularität und das asymptotische Verhalten von Lösungen. Zuletzt befasste er sich mit Integro-Differentialgleichungen der kinetischen Gastheorie (<a href="Boltzmann-Gleichung" title="Boltzmann-Gleichung">Boltzmann-Gleichung</a> und deren Plasmaphysik-Variante, die <a href="Anatoli_Alexandrowitsch_Wlassow" title="Anatoli Alexandrowitsch Wlassow">Vlasov</a>-Gleichung), in Zusammenarbeit mit <a href="Pierre-Louis_Lions" title="Pierre-Louis Lions">Pierre-Louis Lions</a>, und Singularitäten bei inkompressibler Strömung. Mit <a href="Andrew_Majda" title="Andrew Majda">Andrew Majda</a> begann er ab 1986 das Studium der <a href="Eulersche_Gleichungen_(Str%C3%B6mungsmechanik)" class="mw-redirect" title="Eulersche Gleichungen (Strömungsmechanik)">Eulersche Gleichungen</a> in zwei Dimensionen mit Vortices als Anfangsbedingungen und der Frage der Existenz in der Zeit globaler Lösungen (Einführung der <i>Concentration-Cancellation</i> Methode).<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup>

</p><p>Er war <a href="Guggenheim_Fellow" class="mw-redirect" title="Guggenheim Fellow">Guggenheim Fellow</a> und <a href="Sloan_Research_Fellowship" title="Sloan Research Fellowship">Sloan Research Fellow</a>. Er war Invited Speaker auf dem <a href="Internationaler_Mathematikerkongress" title="Internationaler Mathematikerkongress">Internationalen Mathematikerkongress</a> in Berkeley 1986 (<i>Compactness of solutions to nonlinear PDE</i>).

</p><p>Er war mit Maria Schonbeck verheiratet, Professorin für Mathematik an der <a href="University_of_California%2C_Santa_Cruz" title="University of California, Santa Cruz">University of California, Santa Cruz</a>, und hatte eine Tochter.

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<div class="mw-heading mw-heading2"><h2 id="DiPerna_Lectures">DiPerna Lectures</h2></div>

<p>Ihm zu Ehren sind in Berkeley die jährlichen DiPerna Lectures in Angewandter Mathematik benannt, die zuerst 1991 gehalten wurden.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup>

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<ul><li>1991 <a href="Peter_Lax" title="Peter Lax">Peter Lax</a></li>

<li>1992 <a href="Andrew_Majda" title="Andrew Majda">Andrew Majda</a></li>

<li>1993 <a href="James_Glimm" title="James Glimm">James Glimm</a></li>

<li>1994 <a href="Constantine_Dafermos" title="Constantine Dafermos">Constantine Dafermos</a></li>

<li>1995 <a href="Luc_Tartar" title="Luc Tartar">Luc Tartar</a></li>

<li>1996 <a href="Pierre-Louis_Lions" title="Pierre-Louis Lions">Pierre-Louis Lions</a></li>

<li>1997 <a href="Cathleen_Morawetz" class="mw-redirect" title="Cathleen Morawetz">Cathleen Morawetz</a></li>

<li>1999 <a href="Heinz-Otto_Kreiss" title="Heinz-Otto Kreiss">Heinz-Otto Kreiss</a></li>

<li>2000 <a href="Eitan_Tadmor" title="Eitan Tadmor">Eitan Tadmor</a></li>

<li>2001 <a href="Ciprian_Foias" title="Ciprian Foias">Ciprian Foias</a>, <i>Kinetic Formulations of Conservation Laws</i></li>

<li>2002 <a href="Andrew_M._Stuart" title="Andrew M. Stuart">Andrew M. Stuart</a> (Warwick University), <i>Extracting Macroscopic Dynamics</i></li>

<li>2003 <a href="John_M._Ball" title="John M. Ball">John M. Ball</a>, <i>The Regularity of Minimizers in Elasticity</i></li>

<li>2004 <a href="Beno%C3%AEt_Perthame" title="Benoît Perthame">Benoît Perthame</a></li>

<li>2005 <a href="Charles_Fefferman" title="Charles Fefferman">Charles Fefferman</a>, <i>Whitney's extension problem and its variants</i></li>

<li>2006 <a href="Alberto_Bressan" title="Alberto Bressan">Alberto Bressan</a>, <i>Solutions to hyperbolic conservation laws and their approximations</i></li>

<li>2007 <a href="Zheng_Yuxi" title="Zheng Yuxi">Zheng Yuxi</a> (Pennsylvania State University), <i>Multidimensional systems of conservation laws</i></li>

<li>2008 <a href="Gui-Qiang_Chen" title="Gui-Qiang Chen">Gui-Qiang Chen</a> (Northwestern University), <i>Nonlinear Conservation Laws of Mixed Type in Mechanics and Geometry</i></li>

<li>2009 <a href="Andrew_Majda" title="Andrew Majda">Andrew Majda</a>, <i>Applied and Theoretical Challenges for Multi-Scale Hyperbolic PDEs in the Tropics</i></li>

<li>2010 <a href="Lai-Sang_Young" title="Lai-Sang Young">Lai-Sang Young</a>, <i>Mathematics of shear-induced Chaos</i></li>

<li>2011 <a href="Wladimir_Rochlin_(Numeriker)" title="Wladimir Rochlin (Numeriker)">Vladimir Rokhlin</a>, <i>A Randomized Approximate Nearest Neighbors Algorithm</i></li>

<li>2012 <a href="Emmanuel_Cand%C3%A8s" title="Emmanuel Candès">Emmanuel Candès</a>, <i>Exact Phase Retrieval via Convex Programming</i></li>

<li>2013 <a href="Alan_C._Newell" title="Alan C. Newell">Alan C. Newell</a></li>

<li>2014 Takis Souganidis</li>

<li>2015 <a href="Vladim%C3%ADr_%C5%A0ver%C3%A1k" title="Vladimír Šverák">Vladimír Šverák</a></li>

<li>2016 <a href="Gilles_Lebeau" title="Gilles Lebeau">Gilles Lebeau</a></li>

<li>2017 <a href="Herbert_Koch_(Mathematiker)" title="Herbert Koch (Mathematiker)">Herbert Koch</a></li>

<li>2018 Wilhelm Schlag</li>

<li>2019 <a href="Gunther_Uhlmann" title="Gunther Uhlmann">Gunther Uhlmann</a>, <i>Seeing Through Space-Time</i></li></ul>

<div class="mw-heading mw-heading2"><h2 id="Schriften">Schriften</h2></div>

<ul><li><i>Global solutions to a class of nonlinear hyperbolic systems of equations</i>, Comm. Pure Appl. Math. 26 (1973), 1–28</li>

<li><i>Existence in the large for quasilinear hyperbolic conservation laws</i>, Arch. Rational Mech. Anal. 52 (1973), 244–257</li>

<li><i>Uniqueness of solutions to hyperbolic conservation laws</i>, Indiana Univ. Math. J. 28 (1979), 137–188.</li>

<li><i>Convergence of approximate solutions to conservation laws</i>, Arch. Rational Mech. Anal. 82 (1983), 27–70.</li>

<li><i>Convergence of the viscosity method for isentropic gas dynamics</i>, Comm. Math. Phys. 91 (1983), 1–30, <a rel="nofollow" class="external text" href="http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.cmp/1103940470">Online</a></li>

<li><i>Measure-valued solutions to conservation laws</i>, Arch. Rational Mech. Anal. 88 (1985), 223–270.</li>

<li><a rel="nofollow" class="external text" href="http://www.ams.org/journals/tran/1985-292-02/S0002-9947-1985-0808729-4/"><i>Compensated Compactness and general systems of Conservation Laws</i></a>, Transactions AMS, 292, 1985, 383–420</li>

<li>mit Pierre-Louis Lions <i>Global weak solutions of Vlasov-Maxwell systems</i>, Comm. Pure Applied Math., 42, 1989, 729–757</li>

<li>mit Pierre-Louis Lions <i>On the Cauchy problem for Boltzmann equations: global existence and weak stability</i>, Annals of Mathematics, 130, 1989, 321–366</li>

<li>mit Lions: <i>Ordinary differential equations, Sobolev spaces and transport theory</i>, Inventiones Mathematicae, 98, 1989, 511–547</li></ul>

<div class="mw-heading mw-heading2"><h2 id="Weblinks">Weblinks</h2></div>

<ul><li><a rel="nofollow" class="external text" href="http://texts.cdlib.org/view?docId=hb4t1nb2bd&doc.view=frames&chunk.id=div00016&toc.depth=1&toc.id=">Nachruf an der University of California, von Alexandre Chorin, Craig Evans, James Gilman, Andrew Majda</a></li>

<li><a rel="nofollow" class="external text" href="https://zbmath.org/authors/diperna.ronald-j">Ronald J. DiPerna</a> in der Datenbank <a href="ZbMATH" title="ZbMATH">zbMATH</a></li></ul>

<div class="mw-heading mw-heading2"><h2 id="Einzelnachweise">Einzelnachweise</h2></div>

<li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://www.mathgenealogy.org/id.php?id=33317">Ronald DiPerna</a> im <a href="Mathematics_Genealogy_Project" title="Mathematics Genealogy Project">Mathematics Genealogy Project</a> (englisch) <span style="display:none">Vorlage:MathGenealogyProject/Wartung/id verwendet</span></span>

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<li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">↑</a></span> <span class="reference-text">DiPerna, Majda <i>Concentrations in regularizations for 2-D incompressible flow</i>, Comm. Pure Appl. Math. 40 (1987), 301–345, DiPerna, Majda <i>Reduced Hausdorff dimension and concentration-cancellation for two-dimensional incompressible flow</i>, J. Amer. Math. Soc. 1 (1988), 59–95.</span>

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<li id="cite_note-3"><span class="mw-cite-backlink"><a href="#cite_ref-3">↑</a></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://math.berkeley.edu/about/events/lectures/diperna">DiPerna Lectures</a></span>

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