Mathematical Sciences: Properties of Solutions of Linear andNonlinear Partial Integrodifferential 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}
This mathematical research is concerned with a class of                    partial differential equations of second order arising in the                   description of viscoelastic solids or liquids.  The problems                    occupy an intermediate position between the basic parabolic                     partial differential equations for diffusive phenomena and                      hyperbolic equations modeling propagative phenomena.  The goal is               to establish the existence of generalized solutions for arbitrary               initial data under suitable assumptions and to analyze their                    properties.  Specifically, the asymptotic spacial and temporal                  behavior of such solutions is to be studied.  The question of                   whether the damping mechanisms that are inherent in the equations               can be powerful enough to prevent certain discontinuities of the                solutions (corresponding to material instabilities) from                        appearing, will also be taken up.                                                    Specific tasks will include the construction of weak                       solutions in unbounded domains and reflecting problems of shear                 flows of viscoelastic liquids between two plates.  Also,                        solutions of quasilinear equations with nonintegrable kernels                   will be sought.  A passage to the limit of approximate solutions                appears tractable in this setting but has yet to be confirmed.                  The actual smoothness of the resulting weak solution also would                 require study.  A third specific task concerns detailed analysis                of linear equations with variable coefficients.  There is                       evidence suggesting that solutions may actually gain in                         smoothness over their data.  Standard techniques from partial                   differential equations (maximum principle, variational                          characterizations) do not apply, so that new tools will have to                 be developed before progress can be expected.
{'FirstName': 'Hans', 'LastName': 'Engler', 'PI_MID_INIT': 'P', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Hans P Engler', 'EmailAddress': 'engler@georgetown.edu', 'NSF_ID': '000336234', 'StartDate': '07/15/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
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{'Code': '126100', 'Text': 'CLASSICAL ANALYSIS'}
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