“Eco anxiety” is defined as a chronic fear of environmental doom and “ecological grief” is defined as reacting to current and past ecological problems with feelings of anger, guilt, terror, shame anxiety and despair. While they are not considered medical conditions, they have seen a recent rise, particularly in young people. 
According to a global survey of 10,000 young people (aged 16-25) published in September 2021, 59% consider themselves to be very or extremely worried about climate change, over 50% felt sad, anxious, angry, powerless, helpless, and guilty, and over 45% said their feelings about climate change negatively affected their daily life and functioning. 
Part of the reason ecological anxiety and grief are not considered medical conditions by psychologists is that these feelings are quite legitimate as a response to ecological loss and a natural consequence of children on average feeling more empathy for the natural world than adults. Some would say that it is adults and governments who are the ones acting unhealthily and with cognitive dissonance. Many know their actions such as overuse of fossil fuels will damage the environment, yet they do it anyway, this often inspires anger from children who consider this behaviour irrational.
When reporting on this anger and the effects climate change will have on future generations the media often engages in “childism” and makes caricatures of children as rabid activists, innocent victims, or future saviours, none of which is helpful. 
A lot of parents attempt to tame their children’s eco anxiety by simply ignoring it and shutting down discussion of climate change, which is unhelpful and ineffective as the child will remain anxious but will also understand that their parent is unwilling to help them with it. A better strategy is focusing on the action that they can take through climate activism and being more eco friendly in their lives, but that still runs into the problem of individuals ultimately lacking control over what happens with the climate in the future.
Another method is to focus on conquering death anxiety as this usually follows from climate anxiety. Being open about the fact that yes, many species and people will die due to climate change in the future, is much better than distracting ourselves from this difficult truth. Accepting the harsh reality and therefore being more grateful for the life we have right now and marvelling at the fact that we even exist in the first place, is a way for both adults and children to cope with all manner of anxieties about the future, the climate, and death. In addition, understanding and accepting the existential threat created by climate change can help parents take responsibility for their role in causing climate change and work with children to think creatively about way to address it.