Accession Number : AD0671488

Title :   PARTIAL DIFFERENTIAL EQUATIONS, CALCULUS OF VARIATIONS, AND FLUID MECHANICS.

Descriptive Note : Final scientific rept., 15 Sep 67-15 Jun 68,

Corporate Author : MINNESOTA UNIV MINNEAPOLIS DEPT OF MATHEMATICS

Personal Author(s) : Serrin,James B.

Report Date : 18 JUN 1968

Pagination or Media Count : 9

Abstract : The principal investigator completed six research papers during the period September 1967 through June 1968. This work is described in detail in the attached report. The major effort was devoted to nonlinear partial differential equations, the goal being to determine the effect of severe nonlinearity on the soluability of boundary value problems. A classification scheme into regularly elliptic and singularly elliptic equations was obtained by which one can directly determine the degree of nonlinearity of elliptic equations, and corresponding necessary and sufficient conditions of solvability were discovered. In fluid mechanics, the exact asymptotic relationship between Prandtl's boundary layer theory and the full Navier-Stokes equations was established for the case of flows in a radially convergent plane channel. Finally, two papers treated the existence and geometrical behavior of similarity solutions of the boundary layer equations, for free convection near a heated wall and for compressible flows past a boundary surface. (Author)

Descriptors :   (*PARTIAL DIFFERENTIAL EQUATIONS, PROBLEM SOLVING), (*CALCULUS OF VARIATIONS, PROBLEM SOLVING), (*BOUNDARY LAYER, REPORTS), NONLINEAR DIFFERENTIAL EQUATIONS, BOUNDARY VALUE PROBLEMS, NAVIER STOKES EQUATIONS, COMPRESSIBLE FLOW, LAMINAR BOUNDARY LAYER, HYPERSONIC FLOW, THEOREMS

Subject Categories : Numerical Mathematics
      Fluid Mechanics

Distribution Statement : APPROVED FOR PUBLIC RELEASE