Abstract
In this article, global asymptotic stability of solutions of non-homogeneous differential-operator equations of the third order is studied. It is proved that every solution of the equations decays exponentially under the Routh–Hurwitz criterion for the third order equations.
Highlights
There exist numerous studies on the evolutionary PDEs in the literature
Even though there are many works on the stability and instability of solutions to the second-order equations, only a few results are obtained on the stability of solutions to the evolutionary partial differential equations of third order in time
In [1], the authors have considered an abstract initial value problem to prove the stability of solutions with respect to the initial conditions and the right-hand side function f (t)
Summary
There exist numerous studies on the evolutionary PDEs in the literature. works on the differentialoperator equations, especially of the higher order, are rarely encountered [1,2,3] and [4,7]. In [1], the authors have considered an abstract initial value problem to prove the stability of solutions with respect to the initial conditions and the right-hand side function f (t). They obtained global stability results for the non-autonomous second-order differential equations. In [3], Quintanilla and Racke have newly introduced three-phase-lag heat equations in the forms of ρcν T For each equation, they give a suitable Lyapunov function, which is a powerful tool to study the qualitative aspects of the solutions of these equations. It has been shown that every solution to the equation is asymptotically stable, provided that a condition on the function on the right-hand side is established
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