A survey on cauchy problems for peridynamic equations
Kuruk, Gamze (2014) A survey on cauchy problems for peridynamic equations. [Thesis]
The peridynamic theory, proposed by Silling in 2000, is a nonlocal theory of continuum mechanics based on an integro-differential equation without spatial derivatives. This is seen to be main advantage, because it provides a more general framework than the classical theory for problems involving discontinuities or other singularities in the deformation. In this thesis, we present a survey on the well-posedness of the Cauchy problems for peridynamic equations with different initial data spaces. These kind of equations can be also viewed as Banach space valued second order ordinary differential equations. So, in the first part of this study, we recall the theorems about local well-posedness of abstract di erential equations of second order. Then, nonlinear problems related to the peridynamic model are reduced to abstract ordinary di erential equations so that the right conditions can be imposed to imply local well-posedness. In the second part, we study a linear peridynamic problem and discuss the equivalent spaces in which the solution of the problem can take values. We use a functional analytic setting to show the well-posedness of the problem.
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