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Full-Text Articles in Non-linear Dynamics
The Gelfand Problem For The Infinity Laplacian, Fernando Charro, Byungjae Son, Peiyong Wang
The Gelfand Problem For The Infinity Laplacian, Fernando Charro, Byungjae Son, Peiyong Wang
Mathematics Faculty Research Publications
We study the asymptotic behavior as p → ∞ of the Gelfand problem
−Δpu = λeu in Ω ⊂ Rn, u = 0 on ∂Ω.
Under an appropriate rescaling on u and λ, we prove uniform convergence of solutions of the Gelfand problem to solutions of
min{|∇u|−Λeu, −Δ∞u} = 0 in Ω, u = 0 on ∂Ω.
We discuss existence, non-existence, and multiplicity of solutions of the limit problem in terms of Λ.
Mitigating Safety Concerns And Profit/Production Losses For Chemical Process Control Systems Under Cyberattacks Via Design/Control Methods, Helen Durand, Matthew Wegener
Mitigating Safety Concerns And Profit/Production Losses For Chemical Process Control Systems Under Cyberattacks Via Design/Control Methods, Helen Durand, Matthew Wegener
Chemical Engineering and Materials Science Faculty Research Publications
One of the challenges for chemical processes today, from a safety and profit standpoint, is the potential that cyberattacks could be performed on components of process control systems. Safety issues could be catastrophic; however, because the nonlinear systems definition of a cyberattack has similarities to a nonlinear systems definition of faults, many processes have already been instrumented to handle various problematic input conditions. Also challenging is the question of how to design a system that is resilient to attacks attempting to impact the production volumes or profits of a company. In this work, we explore a process/equipment design framework for …
Responsive Economic Model Predictive Control For Next-Generation Manufacturing, Helen Durand
Responsive Economic Model Predictive Control For Next-Generation Manufacturing, Helen Durand
Chemical Engineering and Materials Science Faculty Research Publications
There is an increasing push to make automated systems capable of carrying out tasks which humans perform, such as driving, speech recognition, and anomaly detection. Automated systems, therefore, are increasingly required to respond to unexpected conditions. Two types of unexpected conditions of relevance in the chemical process industries are anomalous conditions and the responses of operators and engineers to controller behavior. Enhancing responsiveness of an advanced control design known as economic model predictive control (EMPC) (which uses predictions of future process behavior to determine an economically optimal manner in which to operate a process) to unexpected conditions of these types …