Bricks, Masonry, Asphalt and Concrete - Damage where slabs meet

My patio is a combination of 2 concrete slabs, one added later up against the original (age of either unknown but original likely 40 plus years).

The original slab is in good shape but the new slab, at the edge where it joins the original, has an issue. At one point there is an area sort of like a valley, approx 24" long, 3/4" wide and 1/2" deep where the concrete has basically crumbled into pieces. At least part of this was caused, or made worse, by water runoff from a flat roof without a gutter. The entire slab is painted with oil based paint.

We want to repaint the slab but I would like to fix this area first if it can be done without putting too much into it in either labor or money. Its almost right up against a wooden screen frame so its not too noticable nor will it often get walked on. I'll be putting gutters up to fix the water issue.

Is there some type of patching material that I can pour into this depression to the slab level and then paint over? Its not a live crack so I think all I really need is something that will adhere to the existing slab and not shrink.

Thanks!

I'm strongly considering using a product called AboCrete.

http://www.abatron.com/home004.htm

Anyone used it?

usually for topcoating or patching concrete i use hydraulic portland cement this is diffrent then regualr portland cement type 10, it wont shrink. mix a little bit of portland up with water untill it becomes the consistancy of think paint and brush it on the surface to be patched make sure you press hard to get into the cracks. make sure it dosnt dry and then mix 2 parts masonry sand or play sand play sand with 1 part portland cement. make it nice and creamy. let it sit for 10 minutes fluff it up again and trowel it on. instead of using the portland wash for adhesive you can also use weldcrete or any bonding agent, just brush it on and wait till it gets tacky then patch, if you use glue or weldcrete make sure to mix a little bit of the glue in with the portland and sand mix this will help bonding,

Thanks for the reply. Have you ever used or heard of the Abocrete stuff? It seems perfect but so far I can't find out if its paintable. Wrote the company but no reply yet.

edit- they replied that it is.