To lessen the intensity of, to mitigate or relieve (hunger, emotion, pain, etc.).
Refreshing winds the summer's heat assuage.
2
To pacify or soothe (someone).
3
To calm down, become less violent (of passion, hunger etc.); to subside, to abate.
Word Origin
From Middle English aswagen, from Old French asuagier (“to appease, to calm”), from Vulgar Latin *assuāviō (“I sweeten, I butter up, I calm”), derived from Latin ad- + suāvis (“sweet”) + -iō.