Could Someone please advise?: well posedness

Nic

Hello forum users, I am reading some reference material at the moment concerning the solution of the equation:

u_t = -f(u)_x {x in range 0 to 1}

boundary conditions: u(x,0) = u0(x),

u(0,t) = p(t),

u(1,t) = h(t).

{where I have said "_" means differentiation and the function f(u) is differentiated with respect to x}

The function of u is defined

f(u)=a1*u^2 - a2(u) {i have a1 and a2 are known constants}

The texts say that the solution is well posed only if

p(t) > u' > h(t)

for some constant value u'.

I have no idea where this condition would be coming from. If someone could please offer an advice I would appreciate it.

Nic