Construction of diffusion processes associated with a porous medium equation (Q913366)

The Cauchy problem, called porous medium equation, \[ (1)\quad u_ t=2^{-1}(u^{\alpha})_{xx},\quad t>0,\quad u(0,x)=u_ 0(x),\quad x\in R, \] for a given \(\alpha >1\), is considered. The diffusion process associated with (1), namely \((X=\{X(t)\},P)\), such that \(P(X(t)\in dx)=u(t,x)dx\) for all \(t\geq 0\), is a weak solution of (1). The author has constructed a class of associated diffusion processes and furthermore given a limit theorem.