US-Federal Republic of Germany Cooperative Research:        Almost Periodicity and Asymptotics for Semigroups of        Operators
{'Code': '01090000', 'Directorate': {'Abbreviation': 'O/D', 'LongName': 'Office Of The Director'}, 'Division': {'Abbreviation': 'OISE', 'LongName': 'Office Of Internatl Science &Engineering'}}
{'SignBlockName': 'Christine French', 'PO_EMAI': None, 'PO_PHON': None}
This award supports Professor W. H. Summers of the University of                Arkansas to collaborate in research with Professor Wolfgang M.                  Ruess of the Mathematics Department, University of Essen, West                  Germany.  In previous joint work, these investigators have combined             complementary backgrounds to develop criteria and techniques which              have proved useful in resolving some longstanding problems by                   providing new insight into dynamical phenomena that are                         asymptotically close to being almost periodic.  The proposed                    cooperative research program will continue this line of                         investigation.  The goal of the research is to identify conditions              on the semigroup, its generator, and the initial values under which             trajectories are asymptotically almost periodic in some appropriate             sense.  Both the expected and existing results in this direction                will be applied to questions concerning the existence and                       description of strong or weak limits of ergodic means, asymptotic               behavior of solutions to the Cauchy problem and functional                      differential equations with infinite delay, and asymptotic behavior             of age-dependent population models.                                                                                                                             Mathematical models for many time-dependent processes in physics,               chemistry and biology take the form of a Cauchy problem associated              with the generator of a semigroup of operators on an appropriate                Banach state space.  The future-time behavior of the process can                then be investigated by studying asymptotic properties of motions               and almost-orbits of the corresponding semigroup.  There has been               considerable effort devoted by many researchers in recent years to              classifying the asymptotic behavior of nonlinear semigroups.  A                 great variety of results has been established by different                      methods.  Drs. Summers and Ruess have brought new techniques and                insights to the problem, and have recently produced some very                   interesting contributions to this subject.  They are now beginning              to seek new applications of their results, in particular to                     nonlinear functional differential equations.
{'FirstName': 'W.', 'LastName': 'Summers', 'PI_MID_INIT': 'H', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'W. H Summers', 'EmailAddress': None, 'NSF_ID': '000372357', 'StartDate': '07/01/1989', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'University of Arkansas', 'CityName': 'FAYETTEVILLE', 'ZipCode': '727013124', 'PhoneNumber': '4795753845', 'StreetAddress': '1125 W MAPLE ST STE 316', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Arkansas', 'StateCode': 'AR', 'CONGRESSDISTRICT': '03', 'CONGRESS_DISTRICT_ORG': 'AR03', 'ORG_UEI_NUM': 'MECEHTM8DB17', 'ORG_LGL_BUS_NAME': 'UNIVERSITY OF ARKANSAS', 'ORG_PRNT_UEI_NUM': None}
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{'Code': '5936', 'Text': 'GERMANY (F.R.G.)'}
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