Sadhu, Susmita
(2011)
Existence and asymptotic analysis of solutions of singularly perturbed boundary value problems.
Doctoral Dissertation, University of Pittsburgh.
(Unpublished)
Abstract
We study existence and uniform asymptotic expansions of solutions of two different classes of singularly perturbed boundary value problems. The first boundary value problem that we consider is ε y' + 2y'+ f(y) = 0, y(0) = y(A) = 0,where f is a smooth, positive increasing function satisfying certain properties and A > 0. We will show that the problem has two solutions for certain values of A. We will also derive and prove a uniform asymptotic expansion of the smaller solution when f(y) = e^y and A = 1. The second boundary value problem that we consider is ε² y' = y(q(x, ε) y), y(1)= α_, y(1)=α_+,where q(x, ε) is a smooth function with uniformly bounded derivatives and is uniformly bounded from below by a positive constant q_∗ for ε sufficiently small. The boundary values α_± are specified positive numbers bounded from above by q_∗. We will derive uniform asymptotic expansion of solutions to this problem that have 3 or fewer critical points.
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Details
Item Type: 
University of Pittsburgh ETD

Status: 
Unpublished 
Creators/Authors: 

ETD Committee: 

Date: 
30 September 2011 
Date Type: 
Completion 
Defense Date: 
19 April 2011 
Approval Date: 
30 September 2011 
Submission Date: 
28 June 2011 
Access Restriction: 
No restriction; Release the ETD for access worldwide immediately. 
Institution: 
University of Pittsburgh 
Schools and Programs: 
Dietrich School of Arts and Sciences > Mathematics 
Degree: 
PhD  Doctor of Philosophy 
Thesis Type: 
Doctoral Dissertation 
Refereed: 
Yes 
Uncontrolled Keywords: 
boundary layers; singular perturbation; uniform asymptotic expansions; variation of constants 
Other ID: 
http://etd.library.pitt.edu/ETD/available/etd06282011194744/, etd06282011194744 
Date Deposited: 
10 Nov 2011 19:48 
Last Modified: 
15 Nov 2016 13:45 
URI: 
http://dscholarship.pitt.edu/id/eprint/8217 
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