Exponential decay of semigroups for second order non-selfadjoint linear differential equations

TL;DR

This paper investigates conditions under which solutions to second order linear differential equations in Hilbert spaces exhibit exponential decay, focusing on operators with specific sectorial and accretive properties.

Contribution

It provides new sufficient conditions ensuring exponential decay for solutions of second order differential equations with sectorial and accretive operators.

Findings

Established criteria for exponential decay of solutions.

Analyzed the role of sectorial and accretive operators in decay behavior.

Extended existing theory to broader classes of operators.

Abstract

The Cauchy problem for second order linear differential equation $u''(t)+Du'(t)+Au(t)=0$ in Hilbert space $H$ with a sectorial operator $A$ and an accretive operator $D$ is studied. Sufficient conditions for exponential decay of the solutions are obtained.