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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|
|Degree Granting Institution:||University of Illinois at Urbana-Champaign|
|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.
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1984.
|Date Available in IDEALS:||2014-12-16|