# Non linear source term in heat equation

**URL:** https://community.freefem.org/t/non-linear-source-term-in-heat-equation/3615
**Category:** General Discussion
**Created:** [December 5, 2024, 11:48am UTC](https://community.freefem.org/t/non-linear-source-term-in-heat-equation/3615 "2024-12-05T11:48:08Z")
**Posts on this page:** 4
**Page:** 1

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### Author: ![441998gg](https://avatars.discourse-cdn.com/v4/letter/4/f04885/32.png) [@441998gg](https://community.freefem.org/u/441998gg)
#### Post date: [December 5, 2024, 11:48am UTC](https://community.freefem.org/t/non-linear-source-term-in-heat-equation/3615/1 "2024-12-05T11:48:08Z")

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Hello everyone,  
I am trying to solve an heat diffusion equation which has a non linear source term. when i am trying to compile it is showing the linear combination error (error operator ( \<10LinearCombI7MGauche4C\_F0E\>, ). I have attached the problem statement along with this message. Thanks for looking into this  
Regards,

 ![image](https://canada1.discourse-cdn.com/flex030/uploads/freefem/original/2X/d/db27db6d755c2c9f2c712b941f5b1eec6f060c9f.png)

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### Author: ![quentin](https://avatars.discourse-cdn.com/v4/letter/q/e47c2d/32.png) [@quentin](https://community.freefem.org/u/quentin)
#### Post date: [December 5, 2024, 11:52am UTC](https://community.freefem.org/t/non-linear-source-term-in-heat-equation/3615/2 "2024-12-05T11:52:32Z")

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Change `pow(dx(T),2)` to `dx(T)*dx(T)` may solve it.

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<div class="post-metadata">

### Author: ![441998gg](https://avatars.discourse-cdn.com/v4/letter/4/f04885/32.png) [@441998gg](https://community.freefem.org/u/441998gg)
#### Post date: [December 5, 2024, 12:16pm UTC](https://community.freefem.org/t/non-linear-source-term-in-heat-equation/3615/3 "2024-12-05T12:16:54Z")

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Hii,  
I have tried that still it’s not working,  
Thanks

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<div class="post-metadata">

### Author: ![quentin](https://avatars.discourse-cdn.com/v4/letter/q/e47c2d/32.png) [@quentin](https://community.freefem.org/u/quentin)
#### Post date: [December 5, 2024, 12:33pm UTC](https://community.freefem.org/t/non-linear-source-term-in-heat-equation/3615/4 "2024-12-05T12:33:45Z")

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Sorry that I made a mistake. Actually, such expression creates a tri-linear term, which is not valid in FreeFEM. You can replace T by Tp, and Tp is T in the previous step:

```auto
dx(Tp)*dx(T)*v//LHS

```

or

```auto
dx(Tp)*dx(Tp)*v//RHS

```