Applied Mathematics Seminar Applied Mathematics SeminarDepartment of Mathematics, Monroe Hall, 2115 G Street NW, Washington, DC 20052.
See the Foggy Bottom campus map.
Contact Maria Gualdani (gualdani at gwu dot edu) or Xiaofeng Ren (ren at gwu dot edu) if you need more information about the seminar.
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.