hello, and welcome to the GMB.
You may be correct with your description of these things - I do know that they are also called 'free-form' bowls, and just possible you may get more hits (to help you) using that name.
Origins for these pieces - probably amongst others - are Denmark (Holmegaard), Sweden (Afors) and China (Ikea), and quality will vary.
The Holmegaard examples designed by Per Lutken, should be signed by the factory, in almost all instances I'd have thought, and I've attached an example showing the details underneath the ground and polished foot, plus one or two other shots of the same bowl - the longest dimension of which is about 16.5 inches (c. 420 mm).
Regret I can't help on the Afors pieces, but according to the books they should show a factory code plus the initials/name of Ernest Gordon who was the designer of their free-form bowl.
Chinese pieces often carry a label, but these are prone to being removed - either accidentally or deliberately.
Does your bowl have a ground/polished depression underneath the foot where the pontil scar has been removed? I could be very wrong, but the marks to which you refer may possibly be from a mould, and providing details of size might help too.