Applied Mathematics Seminar
Thu, 24 September, 2015
9:00pm
Speaker: Jeremy Trageser of GWU
Title: A fourth-order nonlocal operator and its connection with its local counterpart.
Abstract:I will discuss a nonlocal operator as a natural generalization to the biharmonic operator that arises in thin-plate theory. The operator is built in the nonlocal calculus framework and connects with the recent theory of peridynamics. This framework enables us to consider non-smooth approximations to fourth-order elliptic boundary value problems. For these systems I will introduce nonlocal formulations of the clamped and hinged boundary conditions that are well-defined even for irregular domains. Results on well-posedness of these nonlocal problems and regularity of the operator will be given. Lastly, I will outline a proof which demonstrates that when the interaction horizon goes to zero, solutions of the nonlocal problems convergence strongly in L^2 to functions in W^{1,2}. For regular domains we identify these limits as the weak solutions of the corresponding classical elliptic boundary value problems.