Mathematical Sciences: Qualitative Behavior of Solutions    of Elliptic and Parabolic Partial Differential Equations.
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{'SignBlockName': 'John V. Ryff', 'PO_EMAI': None, 'PO_PHON': None}
This work pursues two fundamental problems in the                          mathematical analysis of elliptic and parabolic partial                         differential equations of nonlinear type.  The first concerns the               dynamics of degenerate parabolic reaction diffusion equations.                  These equations occur in models of population dynamics with                     diffusion depending on the density.  The main objective here is                 to construct and classify connecting orbits between equilibria.                 A theory of abstract parabolic equations of DaPrato and Grisvard                will be used in this effort.  A second objective is to determine                when the principle of linearized stability applies and to seek                  replacement principles when it fails.  Application of the                       proposed method has worked successfully in past work on related                 degenerate parabolic equations.  The other main theme, which                    derives from differential geometry, concerns the motion of a                    curve on a surface governed by the curvature vector (of the                     curve).  A parabolic partial differential equation represents the               motion connecting the flow along the curve with the product of                  the normal and the geodesic curvature vectors.  In differential                 geometry, this equation arises formally as the gradient flow of                 the length function.  The equilibria of the differential equation               are the geodesics on the surface.  Earlier results on nodal                     properties of solutions of linear parabolic equations will be                   used in attempts to shed light on the intersection properties of                solutions of the curvature shortening equation.  Related to this                will be the study of intersections of properties of geodesics                   within the same homotopy classes.  Variations of this problem                   occur in the theory of dendrite formation in metallurgy.
{'FirstName': 'Sigurd', 'LastName': 'Angenent', 'PI_MID_INIT': None, 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Sigurd Angenent', 'EmailAddress': 'angenent@math.wisc.edu', 'NSF_ID': '000459021', 'StartDate': '05/15/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'University of Wisconsin-Madison', 'CityName': 'MADISON', 'ZipCode': '537151218', 'PhoneNumber': '6082623822', 'StreetAddress': '21 North Park Street', 'StreetAddress2': 'Suite 6301', 'CountryName': 'United States', 'StateName': 'Wisconsin', 'StateCode': 'WI', 'CONGRESSDISTRICT': '02', 'CONGRESS_DISTRICT_ORG': 'WI02', 'ORG_DUNS_NUM': '161202122', 'ORG_LGL_BUS_NAME': 'UNIVERSITY OF WISCONSIN SYSTEM', 'ORG_PRNT_DUNS_NUM': '041188822'}
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{'Code': '1261', 'Text': 'CLASSICAL ANALYSIS'}
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