Strongly continuous semigroup

Well little one, a strongly continuous semigroup is a fancy way of talking about some operations that happen over time. Think of it like a magic trick that takes place over and over again, but every time it looks a little bit different.

Let's say we have a really special box, and we want to turn it into a different box. We can do this by using a special machine that's connected to the box. This machine can make the box change in different ways, like shrinking it or stretching it.

Now, if we want to change the box a lot, we might need to use the machine many times. And if we want the changes to happen smoothly and continuously, we need to use the machine in a certain way. This is what we mean by a "strongly continuous semigroup." It's a special way of using the machine that makes the box change smoothly over time, even though the changes are actually made in small steps.

Now, this might all sound very complicated, but basically it just means that there's a really special way of making things change over time. And when we want to talk about this special way, we use the words "strongly continuous semigroup." It's a big phrase, but it just means a special way of making changes that happen smoothly and continuously over time.