Modified heat equation with initial conditions

Question

I have to solve the following equation: $$\frac{\partial a(r,t)}{\partial t}=100(D·\frac{\partial^2 a(r,t)}{\partial r^2}-100·a)$$ For different values of D, with r≥0 and with the initial condition $$a(r,t)=Step(1-r)$$ I have studied ODEs but I have never worked on PDEs. Is there enough information to solve the problem?. Or are any other condition needed? I tried to solve it using an ansatz, nevertheless, I can't see how to implement the initial condition to obtain the constants of the solution. I have seen that the Green's function method is useful to solve the heat equation, could it be useful to solve my equation?.

Answer 1

Two Boundary conditions are also required to investigate the problem. You can use the spectral theory to solve the problem. Fourier method is playing a key role in handling such kind of problems.