Random Walks and the Porous Medium Equation
نویسندگان
چکیده
R J(x − y)u(x, t)dy is the rate at which they are leaving location x to travel to all other sites. This consideration, in the absence of external sources, leads immediately to the fact that the density u satisfies equation (1.1). Throughout this note we shall assume also that J is a decreasing radial function whose support is the unit ball. Under these hypotheses we have that individuals that are at a position x are not allowed, with probability 1, to jump to a locations
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