Asymptotic stability of solutions to abstract differential equations

Details Asymptotic stability of solutions to abstract differential equations Asymptotic stability of solutions to abstract differential equations

2010-09-30

arxiv.org/abs/1009.6124v1

Journal of Abstract Diff. Equations and Applications (JADEA), 1, N1, (2010, pp.27-34

Mathematics

Dynamical Systems

Scientific paper

An evolution problem for abstract differential equations is studied. The typical problem is: $$\dot{u}=A(t)u+F(t,u), \quad t\geq 0; \,\, u(0)=u_0;\quad \dot{u}=\frac {du}{dt}\qquad (*)$$ Here $A(t)$ is a linear bounded operator in a Hilbert space $H$, and $F$ is a nonlinear operator, $\|F(t,u)\|\leq c_0\|u\|^p,\,\,p>1$, $c_0, p=const>0$. It is assumed that Re$(A(t)u,u)\leq -\gamma(t)\|u\|^2$ $\forall u\in H$, where $\gamma(t)>0$, and the case when $\lim_{t\to \infty}\gamma(t)=0$ is also considered. An estimate of the rate of decay of solutions to problem (*) is given. The derivation of this estimate uses a nonlinear differential inequality.

Affiliated with

Also associated with

No associations

Rating

Asymptotic stability of solutions to abstract differential equations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Asymptotic stability of solutions to abstract differential equations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Asymptotic stability of solutions to abstract differential equations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-243222