PDE seminar

Speaker: Tadele Mengesha (UTK)

Title: Solvability of a system of nonlocal equations related to peridynamics

Abstract: I will present recent results on solvability of a system of equations that is used in a nonlocal model in mechanics. The nonlocal model is made up of a strongly coupled system of integral equations and is a nonlocal analogue of the Navier-Lame’ system of classical elasticity. 

We will discuss the well-posedness of the system as well as demonstrate optimal local Sobolev regularity of solutions. Connections between the associated nonlocal energy spaces and corresponding classical function spaces will be established. Conditions that imply compact embedding of these spaces in classical spaces will be given. This is a joint work with M. Kassmann and J. Scott.