Date of Award
12-1990
Document Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Department of Mathematics and Statistics
Abstract
A nonlinear partial differential equation, motivated by the transverse vibration of a beam, is shown to have a unique solution. The existence theory, which is in the setting of semigroups and evolution operators, is a composite and synthesis of theorems of Kato. The formulation of the problem and the verification that the formulation leads to a solution are new. The introductory chapter provides background on the topic generally. Chapter 2 provides detailed formulations for the constant coefficient case. Chapter 3 describes nonautonomous cases. The general theorem is presented here. In Chapter 4, a more general case is considered. Namely, Kelvin Voigt damping with a coefficient which depends on the solution. This introduces a nonlinearity to the problem which makes it of the form frequently called quasilinear. This is a stronger form of nonlinearity than semilinear. Results of a numerical example are presented.
AFIT Designator
AFIT-DS-ENC-90-2
DTIC Accession Number
ADA230533
Recommended Citation
Crockett, Carl E., "An Evolution Operator Solution for a Nonlinear Beam Equation" (1990). Theses and Dissertations. 7815.
https://scholar.afit.edu/etd/7815