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Nonlinear Boundary Conditions in Sobolev Spaces

The method of dual steepest descent is used to solve ordinary differential equations with nonlinear boundary conditions. A general boundary condition is B(u) = 0 where where B is a continuous functional on the nth order Sobolev space Hn[0.1J. If F:HnCO,l] —• L2[0,1] represents a 2 differential equation, define *(u) = 1/2 IIF < u) li and £(u) = 1/2 l!B(u)ll2. Steepest descent is applied to the functional 2 £ a * + £. Two special cases are considered. If f:lR —• R is C^(2), a Type I boundary condition is defined by B(u) = f(u(0),u(1)). Given K: [0,1}xR—•and g: [0,1] —• R of bounded variation, a Type II boundary condition is B(u) = ƒ1/0K(x,u(x))dg(x).

Identiferoai:union.ndltd.org:unt.edu/info:ark/67531/metadc332380
Date12 1900
CreatorsRichardson, Walter Brown
ContributorsNeuberger, John W., Mauldin, R. Daniel, Kallman, Robert R.
PublisherNorth Texas State University
Source SetsUniversity of North Texas
LanguageEnglish
Detected LanguageEnglish
TypeThesis or Dissertation
Formativ, 65 leaves, Text
RightsPublic, Richardson, Walter Brown, Copyright, Copyright is held by the author, unless otherwise noted. All rights reserved.

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