# 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**.

This article is incomplete.In particular: "Nonstandard" here corresponds to distributional, viscosity or any other "weak" formulation. In general they are unrelated.You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by expanding it.To discuss this page in more detail, feel free to use the talk page.When this work has been completed, you may remove this instance of `{{Stub}}` from the code.If you would welcome a second opinion as to whether your work is correct, add a call to `{{Proofread}}` the page. |

## 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