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.
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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

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