Abstract :

In the study of parabolic Cauchy problem $u'(t)= Au(t)+f(t), u(0)=x$ on some Banach space $X$, the operator $A$ is assumed to be the generator of analytic semigroup on $X$. More generally $A$ is a sectorial operator whose resolvent set contains some sector in the complex plane. In this talk, we will introduce the sectorial operator, analytic semigroup and how sectorial operator generates an analytic semigroup. Some examples will be given to illustrate these concepts.