About this Event
Speaker: Nicole Buczkowski (University of Nebraska-Lincoln)
Title: Dependence on data and parameters for solutions of nonlocal systems
Abstract: Continuous dependence on data is an important feature for solutions that model physical phenomena. As measurements of physical parameters can never be exact, the goal is to provide a (narrow) range of values for the solutions. The exact dependence can be studied with analysis and partial differential equation tools and serve engineers, computational scientists, and also be important in other theoretical studies.
In this talk, I will discuss these aspects in the nonlocal framework. A main motivation for the increased interest in nonlocal models is their flexibility in handling discontinuities. I will show several results on the continuous dependence (or stability) of the solution with respect to changes in (linear and nonlinear) forcing terms, boundary or collar data, as well as with respect to the kernel of interaction of the nonlocal operator. We will close with some numerical results.
