Consider the following code:
eq1 = D[C1[x, t], t] == D1 D[C1[x, t], {x, 2}];
Initial data and boundary conditions are not consistent. To obtain a numerical result, you must specify the numerical values of all parameters.
I am finally done!
Formulate your task. From your code it is not clear what problem you are trying to solve.
Can I only solve 1st and 2nd PDE with these BC's in Mathematica, because an analytical solution exists by the method of Laplace transform?