Existence of Solutions of a Partial Integrodifferential Equation with Thermostat and Time Delay

Abstract

This paper deals with the mathematical analysis of a retarded partial integrodifferential equation that belongs to the class of thermostatted kinetic equations with time delay. Specifically, the paper is devoted to the proof of the existence and uniqueness of mild solutions of the related Cauchy problem. The main result is obtained by employing integration along the characteristic curves and successive approximations sequence arguments. Applications and perspective are also discussed within the paper.

Stability and Bifurcation Analysis for a Class of Generalized Reaction-Diffusion Neural Networks with Time Delay

“…In this section, we also let the condition ( 1) hold and 1 < 0. And the work of Bianca and Guerrini in papers [4][5][6][7] is the founder of the method in this section. Set = + 0 .…”

The role of time delay in the modeling of fibrosis

“…In particular the time delay has been proposed in population dynamics [3], for immune system response [4-6], tumor growth [7,8], social sciences [9], economics systems [10][11][12][13][14]. Recently time delay has been also proposed in the thermostatted kinetic theory for active particles [15,16].The introduction of a time delay allows to take into account the onset of nonlinear dynamics. Time delay can change the stability of the equilibrium, cause fluctuations, and Hopf bifurcation can occur.…”

“…In particular the time delay has been proposed in population dynamics [3], for immune system response [4-6], tumor growth [7,8], social sciences [9], economics systems [10][11][12][13][14]. Recently time delay has been also proposed in the thermostatted kinetic theory for active particles [15,16].…”