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
Recommended Citation
Bobisud, Larry. "Degeneration of the Solutions of Certain Well Posed Systems of Partial Differential Equations Depending on a Small Parameter." (1966). https://digitalrepository.unm.edu/math_etds/216