Mathematical Sciences: 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 will be done on problems involving nonlinear differential          equations.  The work will focus on three areas.  In the first,                  investigations will be carried out on the relation between Painleve             transcendents and certain linear integral equations arising in inverse          scattering theory.  Certain ordinary differential equations in the              complex plane have only poles for singularities.  These equations, or           transcendents, are related to nonlinear partial differential equations          solvable by the method of inverse scattering.  At this time only                selected examples illustrate the connection but it is clear that an             entire class of equations can be treated.  A systematic study of the            entire relationship will be undertaken.                                                 A second line of research deals with the failure or blow-up of          solutions of nonlinear diffusion equations.  Blow-up of solutions               depends heavily on the nature of initial conditions (as well as the             nonlinearity term in the equation).  Since one is often dealing with            functions of several space variables, blow-up can occur at different            points at different times.  This leads to the main conjecture of the            project: blow-up must be confined to a set of space variables of                negligible size (measure zero).                                                         Third, work will be done on existence, multiplicity and                 asymptotics for combustion theory models with complex chemistry                 including radicals.  The models represent steady planar flame fronts            in premixed combustion.  This analysis goes beyond traditional simple           reactions.  Most models have to confront or hypothesize away what is            known as the cold boundary difficulty to support traveling wave                 solutions.  If intermediate species or radicals are introduced into a           system of reactions, a scheme of the principal investigator leads to            new existence proofs for flame layers.  Work will proceed in expanding          methods developed to cover other complex models, validate their                 asymptotic expansions and consider problems of multiplicity or                  uniqueness.
[{'FirstName': 'Stuart', 'LastName': 'Hastings', 'PI_MID_INIT': 'P', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Stuart P Hastings', 'EmailAddress': 'sph@math.pitt.edu', 'NSF_ID': '000150187', 'StartDate': '07/01/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}, {'FirstName': 'J.Bryce', 'LastName': 'McLeod', 'PI_MID_INIT': None, 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'J.Bryce McLeod', 'EmailAddress': 'mcleod+@pitt.edu', 'NSF_ID': '000334507', 'StartDate': '07/01/1987', 'EndDate': None, 'RoleCode': 'Co-Principal Investigator'}]
{'Name': 'University of Pittsburgh', 'CityName': 'PITTSBURGH', 'ZipCode': '152600001', 'PhoneNumber': '4126247400', 'StreetAddress': '4200 FIFTH AVENUE', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Pennsylvania', 'StateCode': 'PA', 'CONGRESSDISTRICT': '18', 'CONGRESS_DISTRICT_ORG': 'PA18', 'ORG_UEI_NUM': 'MKAGLD59JRL1', 'ORG_LGL_BUS_NAME': 'UNIVERSITY OF PITTSBURGH - OF THE COMMONWEALTH SYSTEM OF HIGHER EDUCATION', 'ORG_PRNT_UEI_NUM': None}
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{'Code': '1261', 'Text': 'CLASSICAL ANALYSIS'}
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1987&All=true', 'xml': '8701356.xml'}