Mathematical Sciences: Solutions to the Grad Differential   Equations as a Limit of Solutions to Free Boundary          Problems
{'Code': '03040100', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'Michael Steuerwalt', 'PO_EMAI': None, 'PO_PHON': None}
The investigator will study the Grad generalized differential              equations which model the equilibrium and slowly varying evolution              of thermonuclear confined plasmas in axisymmetric toroidal devices.             Nonlinear and nonlocal terms enter these equations through                      derivatives of the increasing rearrangement of a function which                 models the poloidal flux of the magnetic field.  The first and                  second derivatives of this flux correspond respectively to magnetic             field and current profiles.  It is important for physical reasons to            determine whether these profiles can develop singularities at the               magnetic axis of the torus.                                                          Professor Laurence will analyze the regularity of minimizers of            a variational formulation of these equations.  He will treat the                case in which the polodial cross section  is convex.  He will                   introduce a set of approximating variational problems and examine               the minimizer of the original variational problem as a limit.  The              m'th approximating problem is a free boundary problem with m free               boundaries.  He will try to extend regularity results for the                   approximating problems to the regularity of a weak solution to the              original problem.                                                                    The increasing rearrangement was first introduced by Hardy,                Littlewood and Polya.  Its properties are of interest in many areas             of analysis, from harmonic analysis to partial differential                     equations and isoperimetric inequalities.  Professor Laurence will              examine how derivates of the rearrangement are affected by isolated             critical points of the underlying function.                                          He will also study convex symmetrization of functions over                 convex domains  or over annuli A with convex boundaries, as well as             certain isoperimetric inequalities related to level set analysis.               The project falls into the general area of applied mathematics, with            applications to plasma physics.
{'FirstName': 'Peter', 'LastName': 'Laurence', 'PI_MID_INIT': None, 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Peter Laurence', 'EmailAddress': 'laurence@mat.uniromal.it', 'NSF_ID': '000127452', 'StartDate': '07/01/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'Pennsylvania State Univ University Park', 'CityName': 'UNIVERSITY PARK', 'ZipCode': '168021503', 'PhoneNumber': '8148651372', 'StreetAddress': '201 OLD MAIN', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Pennsylvania', 'StateCode': 'PA', 'CONGRESSDISTRICT': '15', 'CONGRESS_DISTRICT_ORG': 'PA15', 'ORG_UEI_NUM': 'NPM2J7MSCF61', 'ORG_LGL_BUS_NAME': 'THE PENNSYLVANIA STATE UNIVERSITY', 'ORG_PRNT_UEI_NUM': None}
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{'Code': '1266', 'Text': 'APPLIED MATHEMATICS'}
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