If the lens and the flash of the A590 IS are identical to those in the A580, which is very much likely, then their vignetting / flash coverage characteristics are identical too.
Look at the Flash section on Page 2 of this A580 review: http://www.photographyblog.com …anon_powershot_a580_2.php
It is obvious that there is some corner shading at wide angle even when not using the flash. This is a shortcoming of the lens. The problem is aggravated by the insufficient flash coverage, so if the flash is on and the lens is at the wide end, corner shading can become quite strong.
A work-around to this problem could be purchasing a HF-DC1 digital slave flash, which comes with a flash bracket, so can be attached to your camera. Its coverage might be greater than that of the on-board speedlite.
Another, perhaps cheaper, option is to get rid of the corner shading in an image editor. Photoshop Elements might have a tool for this, but you will want to check it.