Graduate Thesis Or Dissertation
 

A topological approach to dry friction and nonlinear beams

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  • Topological results are applied to boundary value problems modeling nonlinear beams and dry friction. A classical continuation theorem is used to prove existence results for nonlinear beams. Unified proofs, where possible, are given for all the physically relevant boundary conditions. Integration techniques and various integral inequalities are used to prove uniqueness results. Since the equation modeling dry friction exhibits discontinuities in the spatial variable the classical definition of a solution cannot be used; therefore, Filippov's definition of a solution is employed. This definition reformulates the original problem as a differential inclusion. A topological result for set-valued maps is used to prove an existence theorem for periodic solutions of a certain differential inclusion and it is applied to the original problem. Other known results for differential inclusions are also applied to the original equation and to other boundary value problems with discontinuities in the spatial variable.
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