Solve heat problem by using pdepe

I want to solve two boundary condition heat equation changed by time

at t = 0~0.03

pl = ul-15; ql = 0;
pr = ur+20; qr = 0;

at t = 0.03~0.3

pl = ul-15; ql = 0;
pr = ur-80; qr = 0;
c = 1; f = dudx; s = 0; u0 = 15

how can I solve this problem?

Answer 1

[Josh Meyer]

Assuming you want to enforce pr = ur+20; at t=0.03, then you can split the problem into two sub-problems that are solved separately, using the solution of the first problem posed on the interval [0, 0.03] as the initial condition for the second problem posed on the interval [0.03, 0.3].