In this paper, we consider the Burgers’ equation with a time delay. By using the Liapunov function method, we show that the delayed Burgers’ equation is exponentially stable if the delay parameter is sufficiently small. We also give an explicit estimate of the delay parameter in term of the viscosity and the initial condition, which indicates that the delay parameter tends to zero if the initia...

To curb the impact and transmission of worms and virus for simple mass action incidence rate in computer networks, SI1I2RS (Susceptible, Infectious due to worm, Infectious due to virus, Recovered and Susceptible) model have been formed. Basic reproduction number, endemic equilibrium state and their stability are discussed for the simple mass action incidence. For locally and globally asymptotic...

We continue the study of a model for heat conduction [6] consisting of a chain of non-linear oscillators coupled to two Hamiltonian heat reservoirs at different temperatures. We establish existence of a Liapunov function for the chain dynamics and use it to show exponentially fast convergence of the dynamics to a unique stationary state. Ingredients of the proof are the reduction of the infinit...

In this article, we study the piezoelectric beams with thermal and magnetic effects in presence of a nonlinear damping term acting on mechanical equation. First, prove that system is well-posed sense semigroup theory. And by constructing suitable Liapunov functional, show general decay result solution for from which polynomial exponential are only special cases. Furthermore, our does not depend...