Expressions used in Everyday Spoken English in Social and Professional contexts
'Give in' is the phrasal verb meaning to accept something or to agree to something after refusing for a time. To give in can also mean recognise defeat. If you 'give in' it can also mean to concede to do what someone else wants or to be unable to resist temptation.
To give up can also mean to admit defeat or to stop doing something which you usually do regularly. To 'give up' can also refer to stopping a habit that you have formed, for example, to give up smoking. If you give up hope it means to stop thinking or believing in something.