Reactive transport models without mathematical solution

It is well known that not all mathematical equations have a mathematical solution. Also reactive transport models, being actually mathematical equations, may lack a mathematical solution or may have it only in a domain not applicable to the variable (for instance, negative concentrations). Obviously such models cannot represent reality, hence are wrong and should be avoided. Nevertheless, in reactive transport studies the possibility of nonexistence of a solution is seldom taken into account. A reason may be that detection of the existence or nonexistence of a solution is far from obvious, especially for complex models. We studied the existence of a mathematical solution for a number of types of reactive transport models. We found that there are rate laws for kinetic reactions that may lead to models without a solution. Moreover, these are typical rate laws obtained from laboratory experiments. We also propose modifications to these rate laws so that they can be applied to reactive transport models without problems.