I have this PDE with the BCs and ICs
$ u_t=4u_{xx} \\ u(0,t)=u(2,t)=0\quad \text{For All}\quad t>0 \\u(x,0)=f(x) \\ f(x)=10x,\quad x<0,5 \\ f(x)=8,5-7x,\quad 0,5\le x<1,5 \\ f(x)=-8+4x,\quad 1,5\le x< 2$
Please give me some hint for solving this PDE. I know that the BCs is homogeneous, so i can use the separation variable plus fourier series solution. But i'm confused with the ICs. When i can use them all? Please guide me to understand all of this. Thanks and sorry if i have some mistakes.