From an eye-witness BBC reporter:
There are more and more dead bodies on the streets and the stench is unbearable.
Smoke is everywhere.
A house some doors from mine was hit during the bombardment on Wednesday night. A 13-year-old boy was killed. His name was Ghazi.
I tried to flee the city last night but I could not get very far. It was too dangerous.
I am getting used to the bombardment. I have learnt to sleep through the noise - the smaller bombs no longer bother me.
Without water and electricity, we feel completely cut off from everyone else.
I only found out Yasser Arafat had died because the BBC rang me.
It is hard to know how much people outside Falluja are aware of what is going on here.
I want them to know about conditions inside this city - there are dead women and children lying on the streets.
People are getting weaker from hunger. Many are dying from their injuries because there is no medical help left in the city whatsoever.
Some families have started burying their dead in their gardens.
There has been a lot of resistance in Jolan.
The Americans have taken over several high-rise buildings overlooking the district.
But the height has not helped them control the area because the streets of Jolan are very narrow and you cannot fire into them directly.
The US military moves along the main roads and avoids the side-streets. The soldiers do not leave their armoured vehicles and tanks.
If they get fired on, they fire back from their tanks or call in air-strikes.
I saw some Iraqi government soldiers on the ground earlier.
I don't know which part of the country these soldiers are from. They are definitely not from any of the western provinces such as al-Anbar.
I have heard people say they are from Kurdistan.
They are well co-ordinated. When the US forces pull back from an area, the Iraqi soldiers will take over there.
So we trust the Iraqi forces so little that we only dare to send in Kurds - who have been seeking separation, or at least autonomy, from Iraq for decades. This is certainly not going to help the lower the ethnic tension.