Mathematical Sciences: Differential Equations, Continuum    Mechanics and Thermodynamics
{'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 will be done in four related areas of analysis.                    First, radial solutions of nonlinear partial differential                       equations will be sought.  Existence and uniqueness of                          solutions for the ground state problem are of particular                        concern.  Bifurcation problems for positive solutions of the                    Dirichlet problem will be investigated along with a study of                    critical dimensions for the polyharmonic operator.  Asymptotic                  behavior and global structure for the generalized Emden's                       equation will be analyzed and multi-valued ground states for                    the mean curvature operator studied.                                                    Work on the foundations of thermodynamics and continuum                 mechanics focuses on the existence of entropy and internal                      energy, especially as a consequence of non-cyclic                               thermodynamical laws.  A derivation of a generalized energy                     equation for weak first law thermodynamics is planned.                                  Emphasis on shock conditions and shock structure in weak                first law thermodynamics will characterize work on shock wave                   theory.  The Joule-Thompson experiment will be viewed as a                      limiting case of shock wave theory.                                                     A continuation of a fundamental derivation of                           thermodynamics as deduced from mathematical principles will be                  pursued.                                                                                This work relates to several important areas of                         mathematical analysis including nonlinear partial differential                  equations and global analysis.  In addition applications to the                 study of surfaces of prescribed mean curvature, thermodynamics                  and chemical reactions lie close to this undertaking.
{'FirstName': 'James', 'LastName': 'Serrin', 'PI_MID_INIT': 'B', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'James B Serrin', 'EmailAddress': None, 'NSF_ID': '000301685', 'StartDate': '06/15/1987', '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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