# Assigning Well-Posed Boundary Conditions for the Wave Equation

This is not a homework question. I came across this while studying for an exam and I don't know how to answer it. The question is this:

Consider the slightly modified wave equation $$u_{tt} - u_{xx} + u =0, \,\,\,\,\,\, \text{ for } (x,t) \in (0,1) \times (0,\infty)$$ with smooth initial conditions $u(x,0) = \phi(x)$, $u_t(x,0) = \psi(x)$, $x \in (0,1).$ For what choices of real constants $a,b,c,d$ do the boundary conditions \begin{align*} au_x(0,t) + bu_t(0,t) &= 0, \\ cu_x(1,t) + du_t(1,t) &= 0, \,\,\,\,\,\,\, t > 0 \end{align*} lead to a well-posed equation?