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By Andrew Harding
BBC News, Odesa
More than a fortnight after falling under Russian occupation, the residents of Kherson are wrestling with acute shortages of medicine and holding daily protests against the Kremlin's forces. They are also worried that increased shelling on the outskirts might signal the start of a Ukrainian push to recapture their southern city, which is a key port.
A series of loud explosions rattled the windows of Yuri Stelmashenko's office in a government building in the centre of Kherson on Tuesday afternoon, as the city's deputy mayor was on a phone call, busy explaining they had less than a week's supply of food and medicine left.
"Can you hear the shelling outside? Not far off. Unfortunately, we're having to get used to this terrifying reality," said Stelmashenko calmly.
"We're looking at a real humanitarian catastrophe here," he said.
"We've been left here alone - there's no other legitimate authority apart from the mayor. Russian officials came to our office and we agreed that we would continue working. But it's not clear how long that will continue."
There have been reports that Russia might stage a referendum in Kherson on independence from Ukraine - as they previously did in Crimea after it was annexed in 2014, as well in the Russian-backed separatist areas of Donetsk and Luhansk.
But Stelmashenko rejected the idea of this happening in his city, saying it was clear there was no support for Moscow's actions among the largely Russian-speaking population.
Video footage showing a small pro-Russian demonstration in Kherson has been dismissed as a Kremlin propaganda stunt by locals.
On the streets nearby, there were queues for milk, and frustration in local pharmacies which have reportedly run out of most essential drugs.
"There's no medicine left for people with heart conditions, or asthma. The hospitals are working but there's just no medicine," said a medic, speaking by telephone. She asked that we only use her first name, Galina.
"No-one is starving here," said a local university lecturer, Lada Danik, who praised the mayor's office for focusing on trying to support residents of the city without appearing to endorse the Russian occupation.
"The situation is quite stable. We have electricity, water, and there is central heating and transport."
But Danik condemned officials in other occupied cities who have submitted to Russian rule. "If they want to make our city Russian, then it's treason," she said.
In Melitopol, to the east, the Ukrainian mayor was reportedly abducted by Russian forces last week and has not been seen since.
A local pro-Russian official, Danila Galinchenko, has now claimed that she is Melitopol's new mayor and recorded a video message urging residents "to adapt… to the new realities, so we can begin to live in a new way".
But in Kherson, thousands of residents, including Danik, have continued to take part in peaceful daily protests outside government offices in the city centre.
Video footage shows large crowds screaming "fascists… have you no shame?" and "go home" at Russian troops.
"The quantity of soldiers is getting bigger. But they're not military now. They wear different, grey uniform. Like a kind of police," said Danik.
"There were so many people at today's protests that the Russian troops started shooting into the air. It seemed to me they were afraid. I was crying to them: 'Go home, go to your mother.' Two of [the Russian soldiers] were laughing. I was really furious, so I just cried out some curse words.
"I'm not an activist, but I want people to understand what's happening here. I'm in my homeland, not doing anything wrong. I'm trying to protect my daughter."
To the east, another key city, Mykolaiv, has so far managed to hold off a Russian advance.
Mykolaiv's governor, Vitaliy Kim, hinted that Ukrainian forces near Mykolaiv were now looking to recapture Kherson, too.
"Fighting is taking place, clearing out several villages [of Russian forces]…The occupiers are fleeing, and people all say that the troops are running away. It's true. They run," he said in a post on social media.
"Kherson residents, we are with you. Wait! Together we'll be victorious."