3 papers
math.DS2025
Existence and Stability Theory of a Neurologically-Inspired Parabolic PDE Model with a Nonlinear Time-Delayed Boundary Condition
Gangadhara Boregowda, Michael R. Lindstrom
In this paper, we establish the existence of a positive, bounded solution for a class of parabolic partial differential equations with nonlinear boundary conditions, where the boun…
q-bio.NC2024
Oscillations in neuronal activity: a neuron-centered spatiotemporal model of the Unfolded Protein Response in prion diseases
Elliot M. Miller, Tat Chung D. Chan, Carlos Montes-Matamoros +3
Many neurodegenerative diseases (NDs) are characterized by the slow spatial spread of toxic protein species in the brain. The toxic proteins can induce neuronal stress, triggering…
math.AP2024
Local existence of solutions to a nonlinear autonomous PDE model for population dynamics with nonlocal transport and competition
Michael R. Lindstrom
In this paper, we prove that a particular nondegenerate, nonlinear, autonomous parabolic partial differential equation with a nonlocal mass transfer admits the local existence of c…