Mathematical Sciences: Nonlinear Partial Differential       Equations in Plasma Physics
{'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 investigation will focus on the analysis of several                   specific nonlinear hyperbolic partial differential equations                    occurring in plasma physics.  Questions of global solutions to                  the Cauchy problem, stability, possible development of shocks and               collisional effects will be studied for the Vlasov-Maxwell system               of equations.                                                                        Collisionless plasmas are dilute ionized gases.  In them,                  the interaction of particles takes place through the                            electromagnetic field which is generated by the particles                       themselves.  Their trajectories are defined by certain                          differential equations involving relativistically high speeds.                  The principal investigator has shown recently that the Cauchy                   problem for the simpler Vlasov equations has a unique global                    smooth solution provided the momenta of the individual particles                are uniformly bounded.  Work will now be done on models in which                the effects of collisions are taken into account.  Heretofore,                  the electromagnetic effects were allowed to dominate the                        collisional.  No sufficient condition for classical solvability                 is known at this time.                                                               A second line of investigation involves equations with                     rotational symmetry and the question of stability of solutions.                 Certain cases have affirmative answers (i.e. stability is                       confirmed); the applied literature goes further, stating -                      without proof - that stability is present under certain general                 conditions.  What first must be done is a clarification of the                  distinctions, if any, between asymptotic stability and normal                   stability.  Work will be done towards this end.                                      Studies into the open question of the existence of shocks in               collisionless plasma will be carried out.  The work will begin                  with two dimensional problems where fields and densities remain                 bounded for all time.  What is needed now are estimates on the                  derivatives of the fields and densities involved.  There lacks a                Huygens' Principle in two dimensions and it is unclear whether                  this is a real physical barrier (i.e. a shock really occur) or                  is simply a shortcoming of current methods.                                          In addition to its contributions to the theory of partial                  differential equations, this work has important potential                       applications to mathematical physics and statistical mechanics.
{'FirstName': 'Robert', 'LastName': 'Glassey', 'PI_MID_INIT': 'T', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Robert T Glassey', 'EmailAddress': 'glassey@indiana.edu', 'NSF_ID': '000195336', 'StartDate': '05/01/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'Indiana University', 'CityName': 'BLOOMINGTON', 'ZipCode': '474057000', 'PhoneNumber': '3172783473', 'StreetAddress': '107 S INDIANA AVE', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Indiana', 'StateCode': 'IN', 'CONGRESSDISTRICT': '09', 'CONGRESS_DISTRICT_ORG': 'IN09', 'ORG_UEI_NUM': 'YH86RTW2YVJ4', 'ORG_LGL_BUS_NAME': 'TRUSTEES OF INDIANA UNIVERSITY', 'ORG_PRNT_UEI_NUM': 'YH86RTW2YVJ4'}
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{'Code': '1261', 'Text': 'CLASSICAL ANALYSIS'}
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