Ciro Santilli
🔗

Existence and uniqueness of solutions of partial differential equations | 🗖 nosplit | ↑ parent "Differential equation" | 104

🔗
If you have a PDE that models physical phenomena, it is fundamental that:
  • there must exist a solution for every physically valid initial condition, otherwise it means that the equation does not describe certain cases of reality
  • the solution must be unique, otherwise how are we to choose between the multiple solutions?
🔗
Unlike for ordinary differential equations which have the Picard–Lindelöf theorem, the existence and uniqueness of solution is not well solved for PDEs.
🔗
🔗
🔗