Mathematical Sciences: Semilinear Elliptic Equations and    Systems
{'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 on this project combines geometrically motivated                      problems set in an analytic framework.  It represents a                         continuation of research in four areas.  In the first, work will                continue in establishing existence and describing properties of                 conformal metrics with prescribed scalar or Gaussian curvature on               complete manifolds.  This is equivalent to finding positive                     solutions of an elliptic, nonlinear equation on the manifold,                   whose linear term is the Laplace-Beltrami operator in the metric                with scalar curvature appearing as a multiplier of the unknown                  function.  Although much is known about the compact case,                       relatively little has been done in the non-compact setting until                recently.                                                                            A second line of investigation will focus on developing a                  complete understanding of finite mass solutions and infinite                    mass solutions of the Matukuma equations in astrophysics.  These                are semilinear equations, first proposed in 1930, to model the                  dynamics of global star clusters.  These equations are believed                 to be an improvement of Eddington's 1915 model.  The unknown                    function here is the gravitational potential which, for the                     finite total mass case, has only recently been shown to have                    positive entire solutions (the corresponding Eddington equation                 has none).  Many questions remain unanswered regarding  the two                 models and discrepancies observed between their solutions.                           Work will also be done in determining whether the Lane-                    Emden equation of astrophysics has oscillatory as well as non-                  oscillatory solutions and analyzing the asymptotic behavior of                  singular radial solutions.  In addition, relatively recent work                 on chemotaxis has led to new results on solutions of parabolic                  systems describing the oriented movement of cells in response to                chemicals in the environment.  Further work remains in                          determining how the cells move toward places of higher                          concentration and then aggregate.
{'FirstName': 'Wei-Ming', 'LastName': 'Ni', 'PI_MID_INIT': None, 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Wei-Ming Ni', 'EmailAddress': 'wmni@umn.edu', 'NSF_ID': '000274770', 'StartDate': '06/15/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'University of Minnesota-Twin Cities', 'CityName': 'MINNEAPOLIS', 'ZipCode': '554552009', 'PhoneNumber': '6126245599', 'StreetAddress': '200 OAK ST SE', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Minnesota', 'StateCode': 'MN', 'CONGRESSDISTRICT': '05', 'CONGRESS_DISTRICT_ORG': 'MN05', 'ORG_UEI_NUM': 'KABJZBBJ4B54', 'ORG_LGL_BUS_NAME': 'REGENTS OF THE UNIVERSITY OF MINNESOTA', 'ORG_PRNT_UEI_NUM': None}
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{'Code': '1261', 'Text': 'CLASSICAL ANALYSIS'}
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