Create a PDA that accepts the following language
The PDA operates as follows :

Push the symbols you read to the stack

Non-deterministically guess when u ends and w starts

Now for the rest of the string , we consider 2 symbols by 2 symbols , if the 2 symbols are not the same reject , if the 2 symbols are the same , compare them to top of stack , if they are not the same symbol reject , if they are the same pop the stack

After reading the entire input , if the stack is empty accept , else reject


Ex : s = ab bbaa , we push a,b to stack , then we guess u ends and w starts , now we read  b , then b , both are same symbol , we look at top of stack we have  b we pop the b , now the stack has a , and we will read aa , repeat the above again and we accept
If you get how it works , you may want to try to sketch the PDA
Here is a sketch of the PDA to check your answer  :