Intuition behind mild solution

Question

In this question, there is a nice intuitive explanation, why one uses weak solutions and what the intuition is behind the weak solutions: intuition behind weak solution

Is there a similar explanation for mild solutions?

Thank you in advance!

Best,

Luke

Answer 1

See Is a mild solution the same thing as a weak solution? , in which an example is given where a weak solution and mild solution for a particular problem coincide.

Mild solutions are weak solutions in the sense that they are not necessarily classical solutions. They are just a different way of getting a potential classical solution, or a substitute for a classical solution if none exist.