A Note on Heaviside's Expansion Theorem

1940 ◽  
Vol 11 (5) ◽  
pp. 343-346
Author(s):  
F. H. Miller
Keyword(s):  
Expansion Theorem

Wave propagation dynamics in a fractional Zener model with stochastic excitation

2020 ◽  
Vol 23 (6) ◽  
pp. 1570-1604
Author(s):  
Teodor Atanacković ◽  
Stevan Pilipović ◽  
Dora Seleši
Keyword(s):  
Wave Propagation ◽  
Constitutive Equation ◽  
Equations Of Motion ◽  
Weak Form ◽  
Stochastic Excitation ◽  
Expansion Theorem ◽  
Zener Model ◽  
Dissipation Inequality ◽  
Regularity Properties ◽  
Fractional Zener Model

Abstract Equations of motion for a Zener model describing a viscoelastic rod are investigated and conditions ensuring the existence, uniqueness and regularity properties of solutions are obtained. Restrictions on the coefficients in the constitutive equation are determined by a weak form of the dissipation inequality. Various stochastic processes related to the Karhunen-Loéve expansion theorem are presented as a model for random perturbances. Results show that displacement disturbances propagate with an infinite speed. Some corrections of already published results for a non-stochastic model are also provided.

An expansion theorem for eigenvalue problems with several turning points

Analysis ◽  
1993 ◽  
Vol 13 (3) ◽  
pp. 301-308 ◽  
Author(s):  
Walter Eberhard ◽  
Gerhard Freiling
Keyword(s):  
Eigenvalue Problems ◽  
Turning Points ◽  
Expansion Theorem

scholarly journals An extended expansion theorem

1991 ◽  
pp. 29-48 ◽  
Author(s):  
Gian Luigi Ferrari ◽  
Roberto Gorrieri ◽  
Ugo Montanari
Keyword(s):  
Expansion Theorem
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