# A Weak solutions

#### Integrals

Substandard Post - Member warned to provide enough information for people to respond to
What does the colon notation, :, mean?

Last edited:
Related Differential Equations News on Phys.org

#### fresh_42

Mentor
2018 Award
What does the colon notation, :, mean when it is inside an integral for weak solutions?
Can you be a bit more precise and descriptive?

#### Integrals

Can you be a bit more precise and descriptive?
Apologies for the confusion, is it correct to say that $$\mathbf{x}\otimes\mathbf{x}:y$$ is equivalent notation for $$\langle\mathbf{x}\otimes\mathbf{x}, y\rangle$$ where the latter denotes the inner product. Perhaps, this question was more elementary than I had meant...

#### fresh_42

Mentor
2018 Award
I haven't seen the first one, and the second one calls for the question, what are you multiplying there?

#### Integrals

I haven't seen the first one, and the second one calls for the question, what are you multiplying there?
Locally integrable functions - where $$\mathbf{x}=(x_1({\cdot}), x_2({\cdot}), x_3(\cdot))$$

#### WWGD

Science Advisor
Gold Member
How is this related to distributions?

#### fresh_42

Mentor
2018 Award
Locally integrable functions - where $$\mathbf{x}=(x_1({\cdot}), x_2({\cdot}), x_3(\cdot))$$
If I build the $\mathbf{x} \otimes \mathbf{x}$ from this, I get a rank one $3\times 3$ matrix. How can this be multiplied by an $y$ via an inner product, wherever this is from?

#### Haborix

The colon can signify a double dot product (see the wikipedia page on Dyadics). It is still ambiguous what is going on here. What is $y$?

"Weak solutions"

### Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving