Differential-Geometric Methods in the Control of Partial Differential Equations

June 27--July 1, 1999

Boulder, Colorado

A Summer Research Conference of the American Mathematical Society , the Society for Industrial and Applied Mathematics , and the Institute of Mathematical Sciences.

This exploratory Conference will show once more that mathematical research knows no boundaries between specific disciplines -- in this case, analysis versus geometry; and that potentially productive interactions may take place between PDE control theory, the theory of hyperbolic PDEs, and differential geometry. These will be well served by expanding the traditional PDE approaches into fields such as Riemannian geometry. The organizers would like to invite researchers from all three areas to participate in the mathematical explorations and enjoy the glorious natural environment in Boulder.

Click here for the conference schedule.

For local information, including housing, recreation and facilities in Boulder, see the information page at the AMS.

Purposes of this Conference

This conference will explore the infusion of differential-geometric methods into the analysis of control theory problems for partial differential equations (PDEs). Very recent research supports the expectation that Bochner techniques in differential geometry, when brought to bear on the classes of PDE modelling and control problems discussed below, will yield significant mathematical advances. These include:

(a) Intrinsic, coordinate-free models of (non-linear) shell equations, more suitable for mathematical investigation than the present, exceedingly complicated, coordinate-based models, which have been mostly derived in the mechanical literature.

[Technical aspects]

(b) A-priori direct and reverse inequalities for mixed problems for second order hyperbolic PDEs, Maxwell equations, plate-like equations, Schroedinger PDEs (Petrowski-type), defined on a multidimensional euclidean domain, with emphasis on the variable-coefficient case.

[Technical aspects]

(c) Establishment of direct and reverse a-priori inequalities for highly coupled systems of PDEs arising in modern technological applications, such as: shell models and thermo-elastic models defined on two-dimensional surface-like domains; structurally acoustic models defined on acoustic three-dimensional chambers with curved walls, possibly subject to thermo-elastic effects; etc.

[Technical aspects]

These three groups of results are of fundamental importance, because they constitute necessary prerequisites for well-posedness and solvability of control and stabilization problems for the PDE systems described above. The class of problems on shells in (a) above is entirely open; and so are, as a consequence, many of those listed in (c), which depend on the solution of shell problems. As to the problems listed in (b), although a wealth of results has already been obtained, however they refer so far either to the constant-coefficient case or, in the available isolated cases of variable coefficients, the conditions are not readily verifiable, and the proofs are highly technical. Very recent research indicates that, in the general case of variable coefficients, differential (Riemann) geometric methods have the potential to enhance and simplify the presently available theory, as well as to extend it by overcoming remaining difficulties. The time is ripe and propitious, therefore, to further explore in a systematic way new advances along this line of research. Thus, this will be an exploratory, focused, research conference, which will involve both control theory PDE experts and differential geometers interested in PDEs.

Organizers:

Robert Gulliver School of Mathematics, University of Minnesota. gulliver_at_math.umn.edu
Walter Littman, School of Mathematics, University of Minnesota. littman_at_math.umn.edu
Roberto Triggiani Department of Mathematics, University of Virginia. rt7u_at_virginia.edu

Interested mathematicians are urged to register for the conference by sending the following information to the American Mathematical Society, P.O.Box 6887, Providence RI 02940 or to wsd_at_ams.org : title and dates of this conference; your name; mailing address; phone numbers; e-mail address; anticipated arrival/departure dates; scientific background relevant to this conference (indicate if student or if Ph. D. received after 7/1/93); and amount of financial assistance needed, if any. The deadline for registration is Wednesday, March 3th, 1999.

Invited Speakers:

Click on the title to see the abstract and the date and time of the talk
Sagun Chanillo
Rutgers University, New Brunswick
Optimization, free boundary and symmetry breaking problems for the Laplace operator

Jean-Michel Coron
University of Paris-Sud, Orsay, France
On the controllabillity and the stabilizability of incompressible fluids

Michel Delfour
University of Montreal, Quebec, Canada
Modeling and analysis of shell equations (tent.)

José Escobar
Cornell University, Ithaca
An isoperimetric inequality and the first Steklov Eigenvalue

Robert Gulliver
University of Minnesota, Minneapolis
Chord Uniqueness and Controllability: the View from the Boundary

Victor Isakov
Wichita State University, Wichita
Carleman estimates in the uniqueness of continuation, inverse problems, and optimal control

Markus Keel
CalTech, Pasadena
Global Existence of Nonlinear Wave Equations Outside Convex Obstacles

Irena Lasiecka
University of Virginia, Charlottesville
Uniform stabilizability of systems of PDE's coupled at the interface of two regions

John M. Lee
University of Washington, Seattle
On integration by parts

Walter Littman
University of Minnesota, Minneapolis
Boundary control theory and partial differential equations

Jan Sokolowski
Universite Henri Poincare, Nancy, France
Topological derivative for optimal control problems

Giuseppe Tomassini
Scuola Normale Superiore, Pisa, Italy
The Levi equation in Complex Analysis

Francois Treves
Rutgers University, New Brunswick
How Riemannian and subanalytic geometry can help in solving certain overdetermined systems of linear PDE

Roberto Triggiani
University of Virginia, Charlottesville
The infusion of Riemann geometric methods to obtain Carleman inequalities and sharp continuous observability inequalities for variable-coefficient PDEs

Masahiro Yamamoto
University of Tokyo, Japan
Exact observability of a hyperbolic equation of 2nd order in the Neumann case and its applications to inverse problems

Peng--Fei Yao
Academia Sinica, Beijing, China
The Bochner technique and observability inequalities

Participant List

George Avalos

Texas Tech University

avalos_at_mercer.me.ttu.edu

John Cagnol

Ecole des Mines de Paris

John.Cagnol_at_sophia.inria.fr

Sagun Chanillo

Rutgers University

schanillo_at_aol.com

Jean-Michel Coron

University of Paris-Sud

Jean-Michel.Coron_at_math.u-psud.fr

Michel Delfour

University of Montreal

delfour_at_crm.umontreal.ca

Lloyd Douglas

National Science Foundation

ldouglas_at_nsf.gov

Alan Elcrat

Wichita State University

arelcrat_at_twsuvm.uc.twsu.edu

Matthias Eller

Tennessee Tech University

meller_at_tntech.edu

Jose Escobar

Cornell University

escobar_at_math.cornell.edu

Yu-Xin Ge

UFR des Sciences et de la Tech.

Yu.Xin.Ge_at_cmla.ens-cachan.fr

Robert Gulliver

University of Minnesota

gulliver_at_math.umn.edu

Mary Ann Horn

Vanderbilt University

horn_at_math.vanderbilt.edu

Thierry Horsin

Univ. de Versailles Saint-Quentin

horsin_at_math.uvsq.fr

Victor Isakov

Wichita State University

isakov_at_twsuvm.uc.twsu.edu

Guangcao Ji

Texas Tech University

gji_at_math.ttu.edu

Markus Keel

Caltech

keel_at_its.caltech.edu

Irena Lasiecka

University of Virginia

il2v_at_virginia.edu

Catherine Lebiedzik

University of Virginia

John Lee

University of Washington

lee_at_math.washington.edu

Walter Littman

University of Minnesota

littman_at_math.umn.edu

Andrzej Manitius

National Science Foundation

amanitiu_at_gmu.edu

Alexander Shibakov

Tennessee Tech Univ.

ashibakov_at_tntech.edu

Jan Sokolowski

Universite Henri Poincare, Nancy

sokolows_at_iecn.u-nancy.fr

Chiung-Jue Sung

Stanford Univ.

cjsung_at_math.stanford.edu

Giuseppe Tomassini

Scuola Normale Superiore

tomassini_at_sns.it

Francois Treves

Rutgers University

FTreves_at_aol.com

Roberto Triggiani

University of Virginia

rt7u_at_virginia.edu

Masahiro Yamamoto

University of Tokyo

myama_at_ms.u-tokyo.ac.jp

Peng-Fei Yao

Academia Sinica

pfyao_at_iss03.iss.ac.cn

Page maintained by Bob Gulliver

Last Updated on July 14, 1999