Existence and asymptotic analysis of solutions of singularly perturbed boundary value problems

Sadhu, Susmita (2011) Existence and asymptotic analysis of solutions of singularly perturbed boundary value problems. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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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Status:	Unpublished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:	Creators Email Pitt Username ORCID Sadhu, Susmita sus38@pitt.edu SUS38
ETD Committee:	Title Member Email Address Pitt Username ORCID Committee Chair Hastings, Stuart P. sph@math.pitt.edu SPH Committee Member Vainchtein, Anna annav@math.pitt.edu AAV4 Committee Member Ai, Shanbing ais@uah.edu Committee Member Troy, William C troy@math.pitt.edu TROY Chen, Xinfu xfc@math.pitt.edu XINFU
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/etd-06282011-194744/, etd-06282011-194744
Date Deposited:	10 Nov 2011 19:48
Last Modified:	15 Nov 2016 13:45
URI:	http://d-scholarship.pitt.edu/id/eprint/8217

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