@tomleslie Thank you for your advice. I have revised my problem and now have its formulation as follows:
I did't realize about boundary condition for CS(x,0). Sorry for wasting your time. In problem formulation I changed eq5 and eq6 because it originally should be for infinite time, but for this particular problem 10000 sec is an infinite time. eq 10 was wrong, sorry for that. Now it is correct.