##  [Weak Solution](/weak-solution) 

  ##  [Weak Solution](https://natural.quantumdictionary.io/weak-solution-0) 

  

 [![Natural & Formal Sciences Dictionary](/sites/default/files/styles/large/public/2026-01/Natural%20%26%20Formal%20Sciences.png.webp?itok=2kCDRVQv)](/topic-specific-dictionaries/natural-formal-sciences)



**Natural & Formal Sciences Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A function (or equivalence class of functions) that satisfies a differential equation when integrated against a class of test functions, so that derivatives appear in the sense of distributions and boundary conditions are encoded via traces or the test space.

 

 

 

 

 





 

 



 ##  [Weak Solution](https://mathlogic.quantumdictionary.io/weak-solution-1) 

  

 [![Mathematics & Logic Dictionary](/sites/default/files/styles/large/public/2026-01/Mathematics%20%26%20Logic.png.webp?itok=UhtTRPnp)](/topic-specific-dictionaries/natural-formal-sciences/mathematics-logic)

- Natural & Formal Sciences -

**Mathematics & Logic Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A generalized notion of solution in which the governing differential (or integral) equations are satisfied in an integrated or distributional sense against test functions, rather than pointwise; regularity requirements on the candidate function are relaxed so derivatives may exist only in a weak (distributional) sense.