They exist, but it is more common that dinnerware sets have a large dinner plate, a smaller one for salads, and a distinctly deep bowl for soups like the one in this pic. I searched about two dozen sets just now before I found one with a "deep plate" as it's called in Swedish and Italian.
My dinner set has broad, shallow bowls (or deep plates) for beef stew and similar somewhat juicy meals that would be difficult to serve on a plate, a full meal in an almost dinner-plate-sized shallow bowl sometimes set on a dinner plate. "Shallow bowl" describes essentially the same thing as "deep plate."
No, what I meant was that the really bowly-type bowls such as the one in the photo I posted are more common here. But the djupa tallrikar that you show also exists; it's just less common. I suppose an American would call either a bowl, as the term "deep plate" doesn't exist (though it should).
On the US IKEA's website, every deep plate is also a bowl: http://www.ikea.com/us/en/catalog/categories/departments/eating/18862/
On the UK IKEA'S website, most deep plates are not bowls: http://www.ikea.com/gb/en/catalog/categories/departments/eating/18862/
On the french IKEA's website, "assiettes creuses" are never "bols": http://www.ikea.com/fr/fr/catalog/categories/departments/eating/18862/ Same for the irish one: http://www.ikea.com/ie/en/products/tableware/dinnerware/deep-plates/
On the swedish IKEA's website, most "djuppa tallrikar" ar not "skålar": http://www.ikea.com/se/sv/catalog/categories/departments/eating/18862/ Same for the norwegian, danish, english canadian, australian, and french canadian websites.
The USA seems to be the exception here.