Consider the diffusion of particles characterized by the diffusion equation D2C+tn=0, with no sources in a cubical box of size LLL, defined by 0x,y,zL. No particles are allowed to escape, so that all boundaries, at x,y,z=0 or L, are reflecting with vanishing normal component of flux. (a) Explain why all solutions for C(r,t) can be described in the form C(x,y,z,t)=m,n,pcm,n,pcos(kxx)cos(kyy)cos(kzz)ek2Dt, where kx=m/L,ky=n/L,kz=p/L and k2=kx2+ky2+kz2. What values of m,n,p are possible here? Find the solution for an initial distribution of particles C(x,y,z,0) given by C=1 for 0xL/2 and C=0 for L/2