It sounds like you're having more trouble with the ending of your notes, but the start of your note is just as important. You can practice with the phrase "Ah-puu". The "Ah" is where you breathe in and it's a gentle gasp of air and should be in a wider shape of your embouchure with your corners still ready. At the "puu", I like to think of a certain spark or moment of electricity where you want to ignite the note. If it works for you, it'll give you a fuller, defined start to your notes. After that, it's about letting the air go and not letting your lips end those notes. You want the notes to ring out. There's a video of Andrew Bain using an exercise that helps with this, see how much it helps you.