Definition:Differential Equation/Solution/Weak Solution
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Definition
A weak solution is a solution to a non-standard formulation of a differential equation.
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Examples
Distributional Solution
Let $D$ be a differential operator.
Let $T, F \in \map {\DD'} {\R^n}$ be distributions where $F$ is given.
Consider the distributional differential equation:
- $D T = F$
Then $T$ is known as the distributional solution.
Viscosity Solution
Weak Solution/Examples/Viscosity Solution
Also see
- Results about weak solutions can be found here.
Sources
- 2017: Amol Sasane: A Friendly Approach to Functional Analysis ... (previous) ... (next): Chapter $\S 6.3$: A glimpse of distribution theory. Weak solutions