I was wondering what the most used notions for solutions to partial differential equations is in current research. I'm aware, that the concept of solution strongly depends on the specific equation under consideration. But maybe there is a list of different concepts together with the types of equations they apply to.
I know of the following concepts of (generalized) solutions:
- Weak solutions: Used for many different classes of equations.
- Mild solutions: Used for evolution equations.
- Viscosity solutions: Used for first and second order fully nonlinear equations with coefficients satifsying certain monotonicity assumptions.
- Entropy solutions: Used for scalar conservation laws.
- Kinetic solutions: Used for scalar conservation laws.
I would be greatful if you could extend the list with more concepts of solutions that I'm unaware of.
Best, Luke
