Mathematical Sciences: Partial Differential Equations and   Applications
{'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}
This work focuses on a large class of nonlinear partial                    differential equations arising from physical and engineering                    models.  A particular set of problems centers on free boundary                  problems occurring in the study of melting and solidification                   processes, cavity and jet flows and electrochemical processes                   from machining or electroplating.  In such problems, a part of                  the boundary of the domain where the solution is to be found is                 unknown and must be found simultaneously with the solution.                     Substantial progress has been made on problems of this type but                 newer and more realistic models lead to complex equations,                      especially when going from two to three-dimensional                             descriptions.                                                                        Work on optimal design involving free boundaries will also                 be carried out.  These can often be formulated as a minimization                problem for some function of a control in which the solution may                not be differentiable.  Problems of this type occur, for example,               in trying to minimize the pressure in a dam.  The control                       variables appear either in the data or in the coefficients of the               resulting differential equation.  The free boundary conditions                  may occur on a surface which is the control variable.  Recent                   work on construction for an optical lens with certain refraction                properties reduces to solving systems of two nonlinear functional               differential equations.  The construction of a global lens with                 one axis of symmetry which focuses all rays from two sources into               two given collecting points all on the axis has been described                  although it is not clear what happens when not all points are on                the axis of symmetry.  Future work is planned on this equation                  where applications to satellite antenna modeling are expected.
{'FirstName': 'Avner', 'LastName': 'Friedman', 'PI_MID_INIT': None, 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Avner Friedman', 'EmailAddress': 'afriedman@mbi.osu.edu', 'NSF_ID': '000288085', 'StartDate': '07/15/1988', '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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