If a solution to a PDE has a solution f(x) in which f(x) is a Heaviside function, independent on its argument, can I say the solution is unstable, therefore being weak?
2026-03-27 13:45:36.1774619136
Heaviside function and weak solutions
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Yes. Since the PDE has a solution that depends on a Heaviside function, it is discontinous in some parts of its domain, therefore it is not smooth. Being so, the solution does not pass on the stability criteria for a classical (or strong) solution, and so the solution is weak.