Equilibrium solutions of viscous scalar balance laws with a convex flux
The author studies the equilibrium solutions to the problem \[ u_t+ \bigl(f(u)\bigr)_x=\varepsilon u_{xx}+ g(u),\;x\in (0,1),\quad u_x(0)= u_x(1)=0. \] The main result is the calculation of the Morse indices of the hyperbolic equilibrium solutions.
scientific article; zbMATH DE number 1406552