Judging from the yellowing from heat shown in the picture it would appear that cooking pots that are too large for the available space are being used on the back burners that are really for just your 1 or 2 quart pots and percolators. The center burner in the front is the only one safe for use with things like griddles, fry pans and large cooking pots.
You do have to allow enough space between the pots and the Corian or you will burn and crack it. While Corian is heat resistant it will crack, melt and burn if exposed to high heat or flame.
The area with the crack has been exposed to some pretty high temperatures that should not occur unless a pot is getting close to a couple of inches from the counter. Corian can only withstand 212 degrees Fahrenheit without sustaining damage so if heat going around a pot from the burner gets close to it then there will eventually be some discoloring and eventually cracking. They will usually buff out the yellowing and caution you about exceeding the 212 degree limitation of the product at no charge once or twice however they will expect you to refrain from using cookware that is too large for the cooking area after the repair is done. The repairman or service advisor should have covered the possible root causes of this damage (overheating the vertical apron surrounding the stove past 212 degrees so its thermal expansion from being overheated stressed and cracked the main top) with the owner both times it occurred or at least written it down on the service ticket.
Its a tight space so one does have to keep these things in mind, even in a home kitchen, that cooking pots can't be placed too close to counter tops and other materials that can be damaged by heat. That said even stone counter tops will crack if subjected to high concentrated uneven heating.
2001 Winnebago Adventurer WFG35U