How do I assign the result of eval to variable in bash script?
You can cut out the need for grep since you are already using awk. The "$" does not need to be escaped because expansions do not occur inside of single quotes.
pid=$(ps aux | awk -vdate=$(date +%b) '$0 ~ date { print $2 }')If you expect multiple pids to be returned, use an array:
pids=($(ps aux | awk -vdate=$(date +%b) '$0 ~ date { print $2 }'))for pid in "${pids[@]}"; do ...done