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Title:Convergence Properties of the Eigenfunction Expansion of the Biharmonic Equation on Rectangular and Semi-Infinite Strips
Author(s):Challener, David Carroll
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):Mathematics
Abstract:We consider the problem (DELTA)('2)(w(x,y)) = 0, w((+OR-)1,y) = w(,x)((+OR-)1,y) = 0 with boundary conditions w(,xx)(x,0) = f(x) w(,yy)(x,0) = g(x) on the semi-infinite strip -1 (LESSTHEQ) x (LESSTHEQ) 1, 0 < y.
We obtain results on convergence of the eigenfunction expansion resulting from separation of variables. Results are shown when the summability method of Riesz Typical Means is applied to the resulting series and L('p) norm convergence results are given. St. Venant's principle is exhibited along with semi-group properties of solutions and then all results are applied to rectangular regions.
Issue Date:1984
Type:Text
Description:151 p.
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1984.
URI:http://hdl.handle.net/2142/71222
Other Identifier(s):(UMI)AAI8502093
Date Available in IDEALS:2014-12-16
Date Deposited:1984


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