Category of a PDE and its properties

Question

Now I am working on numerical method for a PDE. I am considering the following PDE: $$ u_t+a^2u_{xx}=f\\ u(x,0)=u_0\\ u(x,t)|_\Gamma=u_g $$ That equation seems very like heat equation which only change a sign of $u_{xx}$ item. I am wondering that is this a kind of parabolic equation? For the definition, the answer seems right. But there no references introduce the properties about it (such as mean value principle and maximum value principle). I just make a program to compute the numerical solution about it and the numerical result shows not very stable. Could any one can introduce some about this equation or tell me which book have the introduction? Thanks in advance.