Mathematical Sciences: Operator Theory and Differential     Equations
{'Code': '03040102', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'John V. Ryff', 'PO_EMAI': None, 'PO_PHON': None}
Work supported by this award will focus on a variety of                    mathematical topics approached from a point of view which                       emphasizes techniques from functional analysis and the tools of                 nonlinear operator semigroups.  Three problem areas will be                     addressed.  The first, quantum theory, involves properties of                   ground state electron densities and several variants of Thomas-                 Fermi theory dealing with spin polarized systems, exchange                      corrections, inverse problems and nuclear theory.  Nonlinear                    partial differential equations represent the spin polarized                     Thomas-Fermi theory of generalized atoms.  Work will be done to                 minimize the interaction of pairs of chemical potentials.  The                  Euler-Lagrange equations for the energy functional yield a                      coupled elliptic system which remains to be analyzed.                                A second line of research on semigroups of operators                       concerns a Hille-Yosida type theory for certain first and second                order semilinear evolution equations.  Work will concentrate on                 finding necessary and sufficient conditions on semilinear                       equations to guarantee not only a strongly continuous semigroup                 of operator solutions but also to obtain growth conditions on                   solutions in terms of prescribed functionals.  Related work will                be concerned with continuing investigations into equipartition of               energy, approximation theorems, ergodic theory and two-point                    boundary problems.                                                                   The third area, nonlinear partial differential equations,                  concerns model equations arising in fluid dynamics and biology.                 The equations are nonlinear degenerate parabolic boundary value                 problems; the object of the work is to determine when the                       corresponding abstract differential operator is dissipative.
{'FirstName': 'Jerome', 'LastName': 'Goldstein', 'PI_MID_INIT': 'A', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Jerome A Goldstein', 'EmailAddress': 'jgoldste@memphis.edu', 'NSF_ID': '000203852', 'StartDate': '06/15/1989', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'Tulane University', 'CityName': 'NEW ORLEANS', 'ZipCode': '701185665', 'PhoneNumber': '5048654000', 'StreetAddress': '6823 SAINT CHARLES AVE', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Louisiana', 'StateCode': 'LA', 'CONGRESSDISTRICT': '01', 'CONGRESS_DISTRICT_ORG': 'LA01', 'ORG_UEI_NUM': 'XNY5ULPU8EN6', 'ORG_LGL_BUS_NAME': 'ADMINISTRATORS OF THE TULANE EDUCATIONAL FUND, THE', 'ORG_PRNT_UEI_NUM': 'XNY5ULPU8EN6'}
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{'Code': '1261', 'Text': 'CLASSICAL ANALYSIS'}
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1989&All=true', 'xml': '8900134.xml'}