University of Illinois Urbana-Champaign

Convergence Properties of the Eigenfunction Expansion of the Biharmonic Equation on Rectangular and Semi-Infinite Strips

Challener, David Carroll

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https://hdl.handle.net/2142/71222

Description

Title
Convergence Properties of the Eigenfunction Expansion of the Biharmonic Equation on Rectangular and Semi-Infinite Strips
Author(s)
Challener, David Carroll
Issue Date
1984
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(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.
Graduation Semester
1984
Type of Resource
text
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http://hdl.handle.net/2142/71222

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