Nonlinear Hyperbolic Equations, Elasticity
{'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 project continues and expands upon earlier work                       focusing on the formulation of singularities in solutions of                    nonlinear hyperbolic equations.  In particular recent new                       developments related to systems will be continued.  The immediate               aims are to obtain asymptotic estimates for the time when the                   first singularity occurs.  This point is frequently referred to                 as the moment of blow-up.                                                            Initial conditions involve data of compact support of fixed                shape and size.  The immediate aim of this work is to obtain                    asymptotic estimates for the time at which blow-up occurs based                 on the initial size.  Earlier work on the nonlinear wave equation               and systems of elasticity equations only produced lower bounds                  for this critical time.  Projected work will be concerned with                  the derivation of supplementary upper limits which would, in                    turn, imply blow-up in finite time.  In addition to these                       estimates work will be done in analyzing the behavior of                        solutions near blow-up time.  While these questions are                         relatively simple in one space dimension, the situation for                     general three-dimensional solutions is much more complicated.                   One will have to analyze the extent to which higher angular                     derivatives may eliminate contributions from lower radical ones.                     Efforts will also be made to understand long-term behavior                 of quasilinear systems which reduce to homogeneous linear systems               with constant coefficients for infinitesimal solutions.  An                     example of this type of problem arises in the study of finite                   amplitude waves in an unistropic hyperelastic material.
{'FirstName': 'Fritz', 'LastName': 'John', 'PI_MID_INIT': None, 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Fritz John', 'EmailAddress': None, 'PI_PHON': None, 'NSF_ID': '000236263', 'StartDate': '07/01/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'New York University', 'CityName': 'NEW YORK', 'ZipCode': '100121019', 'PhoneNumber': '2129982121', 'StreetAddress': '70 WASHINGTON SQ S', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'New York', 'StateCode': 'NY', 'CONGRESSDISTRICT': '10', 'CONGRESS_DISTRICT_ORG': 'NY10', 'ORG_UEI_NUM': 'NX9PXMKW5KW8', 'ORG_LGL_BUS_NAME': 'NEW YORK UNIVERSITY', 'ORG_PRNT_UEI_NUM': 'NX9PXMKW5KW8'}
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{'Code': '1261', 'Text': 'CLASSICAL ANALYSIS'}
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