What kind of partial differential equation is this？
$$\frac{\partial u(x,t)}{\partial t}-\frac{\partial ^2u(x,t)}{\partial x^2}=r(t)u(x,t)+f(x,t)$$ I would like to know how to describe this equation and where does this equation come from.
Solution 1:
This is linear reaction-diffusion equation. It commonly appears in modelling of chemical reactions.