Author

Larry Bobisud

Publication Date

4-21-1966

Abstract

Let be a system of N partial differential equations, where α is a multi­index, p is a positive number, the Bα are N x N matrices of constants, A(ϵ) is an N X N diagonal matrix with N-m ϵ's followed by m ones (1 ≤ m ≤ N-1), and For each ϵ > 0 Vϵ is to satisfy V(0, x) = f(x). Under sufficiently strong assumptions on (1), this problem can be solved for each sufficiently small ϵ > 0 provided f has a sufficient number of L1 and continuous derivatives. Let M1 denote the upper left (N - m) x (N - m) submatrix of Then if |det M1()|≥k for some constant k > 0 the degenerate problem obtained from (1) by setting ϵ = 0 can also be solved uniquely with the solution U satisfying U2(0, x) = f2(x), where for any N-vector y we denote by y2 the m-vector formed by taking the last m entries of y. By means of the Fourier transform we study the question of when the behavior Vϵ = U + boundary layer terms + quantities which go to zero with ϵ obtains as ϵ → 0.

Degree Name

Mathematics

Level of Degree

Doctoral

Department Name

Mathematics & Statistics

First Committee Member (Chair)

Reuben Hersh

Second Committee Member

Burt Jules Morse

Third Committee Member

Julius Rubin Blum

Language

English

Document Type

Dissertation

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