Hi, SeriousMax.
Welcome to the Apple Support Communities. We’re glad you decided to reach out about the display on your iPhone 11. If we understand correctly, after your iPhone stays on the same image for a couple of minutes it seems like it displays remnants of the picture on your screen for a few hours.
You may be experiencing a behavior sometimes called “image persistence” that can occur with the newer technology of our displays. It’s expected that the display show a faint remnant of a high contrast image that is continuously displayed for a prolonged period of time. Your iPhone is designed to use the brightness aspect of your display to reduce those visual effects, but as your iPhone display ages it may experience reduced brightness levels as it ages, which will reduct the effects that Apple has put into place to counter the image persistence from the newer display.
You can read more about these features in this Apple Support article:’
About the Super Retina display on your iPhone X, iPhone XS, and iPhone XS Max, and the Super Retina XDR display on your iPhone 11 Pro and iPhone 11 Pro Max - Apple Support
All our best.