Mathematical Sciences: Nonlinear Mathematical Transport     Theory and Population Models
{'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 will focus on the investigation of nonlinear                     partial integro-differential and integro-difference equations                   which arise from mathematical transport theory and population                   models.  In the former, studies of the general transport process                describing the effects of collision, absorbtion and reflection of               molecules or particles in gases whose kinetics is governed by the               nonlinear Boltzman equation are carried out.  Problems of                       existence, uniqueness continuous dependence on initial data,                    smoothness, approximation and asymptotic behavior for large time                will be undertaken.  Techniques will employ the theory of                       abstract differential equations in ordered Banach spaces and                    lattices, strongly continuous operator semigroups and path                      integrals.  Specific models associated with the kinetic behavior                of gases where collisions are governed by general interaction                   potentials will be considered.                                                       Work on population dynamics will utilize the discrete time                 nature of a growth-dispersal process whose evolution is described               by a dynamical system modeling competition among species living                 in the same habitat.  Interaction assumptions have two                          qualitative forms: peaceful competition or predator-prey                        competition.  Fundamental concerns in this work are the                         establishment of conditions for coexistence of species and                      obtaining optimal dispersion strategies for the individual                      species.  The mathematical context for this work is the spectral                theory of positive operators applied to Frechet derivatives, in                 studying solutions of Hammerstein equations which relate growth                 and dispersion.
{'FirstName': 'Peter', 'LastName': 'Takac', 'PI_MID_INIT': None, 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Peter Takac', 'EmailAddress': None, 'NSF_ID': '000381774', 'StartDate': '05/15/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'Vanderbilt University', 'CityName': 'NASHVILLE', 'ZipCode': '372032416', 'PhoneNumber': '6153222631', 'StreetAddress': '110 21ST AVE S', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Tennessee', 'StateCode': 'TN', 'CONGRESSDISTRICT': '05', 'CONGRESS_DISTRICT_ORG': 'TN05', 'ORG_UEI_NUM': 'GTNBNWXJ12D5', 'ORG_LGL_BUS_NAME': 'VANDERBILT UNIVERSITY', 'ORG_PRNT_UEI_NUM': None}
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{'Code': '1261', 'Text': 'CLASSICAL ANALYSIS'}
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