CONVERGENCE RESULTS FOR A CLASS OF NONLINEAR FRACTIONAL HEAT EQUATIONS

Abstract

In this article we study various convergence results for a class of nonlinear fractional heat equations of the form ⎧⎨ ⎩ ut(t, x)− I[u(t, ·)](x) = f(t, x), (t, x) ∈ (0, T) × Rn, u(0, x) = u0(x), x∈ Rn, where I is a nonlocal nonlinear operator of Isaacs type. Our aim is to study the convergence of solutions when the order of the operator changes in various ways. In particular, we consider zero order operators approaching fractional operators through scaling and fractional operators of decreasing order approaching zero order operators. We further give rate of convergence in cases when the solution of the limiting equation has appropriate regularity assumptions.