HOW LONG DOES IT TAKE FOR A GAS TO FILL A POROUS CONTAINER

Let us consider the problem u(t)(x, t) = Delta u(m)(x, t) for (x,t) ep silon D x [0, +infinity), u(x, 0)= u(0)(x) for x epsilon D, and (parti al derivative u(m)/partial derivative n)(x, t) = h(x, t) for (x, t) ep silon partial derivative D x [0, +infinity). Here we assume D subset o f R(N), m > 1, u(0) greater than or equal to 0,and h greater than or e qual to 0. It is well known that solutions to this problem have the pr operty of finite speed propagation of the perturbations. By this we me an that if z is an interior point of D and exterior to the support of u(0), then there exists a time T(z) > 0 so that u(z, t) = 0 for t < T( z) and u(z, t) > 0 for t > T(z). In this note we give, in an elementar y way, an upper bound for T(z) for the case of bounded convex domains and in the case of a half space.