Mathematical Sciences: Stability for Reaction-diffusion     Equations
{'Code': '03040101', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'John V. Ryff'}
This project will follow two lines of investigation into                   problems of applied mathematics.  The first is that of                          understanding certain mathematical models for phase transition                  phenomena.  The problems have a variational structure and involve               the study of distinguished solutions for elliptic or parabolic                  equations with small diffusion coefficients.  The second category               of work will concentrate on evolution systems that are not                      necessarily of variational type and which preserve order.  One                  main objective is to determine asymptotic properties of all                     solutions.                                                                           A common theme which ties the research together is that the                problems deal with reaction-diffusion mechanisms and that the                   analysis employs stability considerations.  From the applications               point of view, the first project seeks to model certain                         observable patterns either as stable equilibria or as unstable                  manifolds of equilibria; the second seeks to exclude the                        possibility of stable chaos for classes of forced systems and to                establish very regular behavior criteria.
{'FirstName': 'Nicholas', 'LastName': 'Alikakos', 'EmailAddress': 'alikakos@unt.edu', 'StartDate': '06/01/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'University of Tennessee Knoxville', 'CityName': 'Knoxville', 'ZipCode': '379163801', 'PhoneNumber': '8659743466', 'StreetAddress': '1331 CIR PARK DR', 'CountryName': 'United States', 'StateName': 'Tennessee', 'StateCode': 'TN'}
{'Code': '1266', 'Text': 'APPLIED MATHEMATICS'}
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1988&All=true', 'xml': '8804631.xml'}