Large time behavior of exchange-driven growth

Exchange-driven growth.

We study a class of growth processes in which clusters evolve via exchange of particles. We show that depending on the rate of exchange there are three possibilities: (I) Growth-clusters grow indefinitely, (II) gelation-all mass is transformed into an infinite gel in a finite time, and (III) instant gelation. In regimes I and II, the cluster size distribution attains a self-similar form. The la...

Large Time Behavior of Boosting

1 2 We exploit analogies between regression and classiication to study certain properties of boosting algorithms. A geometric concept called the angular span is deened and related to analogs of the VC dimension and the pseudo dimension of the regression and classiication systems, and to the assumption of the weak learner. The exponential convergence rates of boosting algorithms are shown to be ...

Large Time Behavior of Solutions of a

We study the large time behavior of solutions of the Cauchy problem for a fast di usion equation with a singular powerlike source. It is shown that the large time behavior is described by the similarity solution of related problem.

On the Large Time Behavior of Solutions

Large Time Behavior of Solutions to SemiLinear Equations with Quadratic Growth in the Gradient

This paper studies the large time behavior of solutions to semi-linear Cauchy problems with quadratic nonlinearity in gradients. The Cauchy problem considered has a general state space and may degenerate on the boundary of the state space. Two types of large time behavior are obtained: i) pointwise convergence of the solution and its gradient; ii) convergence of solutions to associated backward...