  We consider a generalized Burger's equation (dtu = dxxu - udxu + up -
{\lambda}u)in a subdomain of R, under various boundary conditions. First, using
some phase plane arguments, we study the existence of stationary solutions
under Dirichlet or Neumann boundary conditions and prove a bifurcation
depending on the parameters. Then, we compare positive solutions of the
parabolic equation with appropriate stationary solutions to prove that global
existence can occur for the Dirichlet, the Neumann or the dissipative dynamical
boundary conditions {\sigma}dtu+d{\nu}u = 0. Finally, for many boundary
conditions, global existence and blow up phenomena for solutions of the
nonlinear parabolic problem in an unbounded domain are investigated by using
some standard super-solutions and some weighted L1-norms.
