Homogenization of fundamental solutions for parabolic operators involving non-self-similar scales (Q6618010)

This paper studies the asymptotic expansion of the fundamental solutions for second-order parabolic operators with non-self-similar scales\N\[\N\partial_tu-\mathrm{div}(A(x/\varepsilon, t/\varepsilon^\ell)\nabla),\N\]\Nwhere \(A(z, \tau)\) is periodic in \((z, \tau)\) and \(\ell\neq 2\). The asymptotic expansions, up to second-order derivatives, are established based on the quantitative two-scale expansions and some weighted estimates.