Singularity Propagation for the Gurtin-Pipkin equation
Sergei Ivanov
TL;DR
This paper investigates how a Dirac delta boundary condition in the Gurtin-Pipkin equation leads to a moving delta function that diminishes exponentially over time, revealing new dynamic behavior.
Contribution
It introduces the concept of singularity propagation in the Gurtin-Pipkin equation, showing how boundary delta functions evolve.
Findings
Moving delta function with exponential decay
Boundary delta causes internal singularity propagation
New dynamic behavior in Gurtin-Pipkin models
Abstract
We show that the Dirac delta function in the boundary condition of the Gurtin-Pipkin equation generates a moving delta-function with an exponentially decreasing factor.
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Taxonomy
TopicsStability and Controllability of Differential Equations · Advanced Mathematical Physics Problems · Advanced Mathematical Modeling in Engineering