Large time behaviour of solutions of a singular diffusion equation in image Original Research Article

Let A>0A>0, n⩾2>qn⩾2>q, n/20u>0, in Rn×(0,∞)Rn×(0,∞), u(x,0)=u0(x)u(x,0)=u0(x) in RnRn and ψψ is the unique self-similar solution of the equation with initial value A|x|-qA|x|-q. Then the rescaled function v(x,t)=tq/(2-q)u(t1/(2-q)x,t)v(x,t)=tq/(2-q)u(t1/(2-q)x,t) will converge uniformly on every compact subset of RnRn to ψ(x,1)ψ(x,1) as t→∞t→∞.