i did simplify and each time work but this time is give me another thing can anyone find what is problem?

pdetest2.mw

in here i did exactly the same but i am not sure the author did something mistake or i did becuase one term in the pde is change and how exactly do that replacement in eq62?

S.mw

i did try and even replace the function w(t) by anotehr thing but is not working  how i can find that and make be answer of my pde?

k1.mw

How can find thus parameters 

Dr.D-problem.mw

a million time i try to figure out how i can get this plot ? why my graph  in countor is not same the 3D plot? where is problem?

Bgraph1.mw