HOW LONG DOES IT TAKE FOR A GAS TO FILL A POROUS CONTAINER
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Date
1994
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AMER MATHEMATICAL SOC
Abstract
Let us consider the problem u(t)(x, t) = Delta u(m)(x, t) for (x,t) epsilon D x [0, +infinity), u(x, 0)= u(0)(x) for x epsilon D, and (partial derivative u(m)/partial derivative n)(x, t) = h(x, t) for (x, t) epsilon partial derivative D x [0, +infinity). Here we assume D subset of R(N), m > 1, u(0) greater than or equal to 0,and h greater than or equal to 0. It is well known that solutions to this problem have the property of finite speed propagation of the perturbations. By this we mean 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 elementary way, an upper bound for T(z) for the case of bounded convex domains and in the case of a half space.
In this note we give, in an elementary way, an upper bound for T(z) for the case of bounded convex domains and in the case of a half space.
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Keywords
DIFFUSION, POROUS MEDIA, MEDIUM EQUATION