Passover dishes mixed with Chametz dishes Rabbanit Batya Krauss

When kitchenware (utensils/dishes/pots/pans etc.) of any kind is mixed in with Pesach kitchenware and there is no way to differentiatebetween them there are a couple of halachic questions we must answer:
1. Can the items in question be used without kashering?
2. If kashering is required, are the dishes made from a material that can be kashered?
There are several halachic issues here.
1. In cases such as this one option is using the halachic concept of nullification – ביטול. In general. when prohibited food is accidentally mixed with permitted food and is now indiscernible it may be permitted to be eaten by “nullifying” the prohibited food if the mixture contains a certain ratio of prohibited to permitted food. The question here is whether this rule for food also applies to kitchenware? 
2. Even if the rules of nullification apply to kitchenware, they may not apply in this case as the sages were stringent with chametz on Pesach and ruled אפילו באלף לא בטיל – it is not nullified, even by 1:1,000 ration. There are two reasons for this stringency.
a. Chamtez is a Torah prohibition and transgression carries the punishment of karet. 
b. Chametz is included in the halachic category of דבר שיש לו מתירים , something that can be permitted – in this case after Pesach it is permitted – and therefore it is not subject to rules of nullification.
3. Can porcelain be kashered or does it have the same rules as earthenware, which can’t be kashered?
Explaining the issues:
1. Is kitchenware subject to the halachic rule of nulification?
When a dry piece of prohibited food is mixed with two identical pieces of permitted food, the minority of prohibited food is nullified by the majority – בטל ברוב – (Shulchan Aruch YD 109). In the case of kitchenware the Shulchan Aruch rules that “a vessel forbidden due to absorbing prohibited food that was then mixed with other vessels and is unrecognizable is nullified by the majority) (YD 122:8) This teaches us that a non-kosher piece of kitchenware that was mixed with kosher ones is nullified by the majority of kosher ones and may be used without koshering. The Shach and Taz note that it is preferable to kasher the dishes in this case.
Additionally, based on a discussion about the status of dairy and meat dishes that were found together and/or washed together the Be’er Hetev rules that the dished can be used after waiting 24 hours, so that any taste absorbed into the dishes would be considered to give off an unappetizing taste נותן טעם לפגם, which is no longer a Torah prohibition. (Be’er Hetev YD 102:6)

2. The problem of using the laws of ביטול for Pesach:
The Shulchan Aruch rules that while there is no ביטול on Pesach itself, there is ביטול before Pesach and what was nullified before Pesach remains nullified on Pesach. The Rama expresses concern that the prohibition that was nullified may return to its prohibited state on Pesach when the rules of ביטול no longer function as usual (חוזר וניעור). While the Rama urges stringency the Mishnah Berurah rules that the one may hold by ביטול if the chamtez is:
a. not from within the last 24 hours (אינו בן יומו)
b. not independently substantive, but has been absorbed into something else
c. would interferes with the joy of the festival and was mixed before Pesach.
All these conditions are fulfilled in our case.
2b. דבר שיש לו מתירים
While some may be concerned that the laws of ביטול should not apply to the dishes as they  are דבר שיש לו מתירים, since they can be used when it is not Pesach, this does not seem to be a problem. The Shulchan Aruch (YD 102:3) states that a vessel that was used with prohibited foods and absorbed their taste, and was subsequently mixed with permitted kitchenware is not considered  דבר שיש לו מתירים because there are expenditures involved in kashering it. Additionally, The Pitchei Teshuva brings Rav Yechezkel Landa who explains that the concept of דבר שיש לו מתירים applies to food, but not to kitchenware.

3. Porcelain dishes
It is generally accepted that ceramic dishes can’t be kashered. However, Rav Ovadiah Yosef rules that in cases where this would lead to a severe financial loss the dishes can be kashered by doing הגעלה three successive times. (Shut Yabia Omer Part 1 YD 6, The Ba’al Ha’Itur has a similar opinion) While the Chatam Sofer does not bring the option of הגעלה he rules that after a year of sitting unused any prohibited taste absorbed in dishes becomes like dust and is nullified. Finally, Rav Moshe Feinstein (YD Part I 43) also rules that under certain circumstances one can do הגעלה to change dairy dishes over to meat and vice versa.