不可压渗流方程解的衰减估计

摘要

A decay rate of the solution was derived to the incompressible porous medium equations governed by Darcy's law, with the property of the semigroup operator e-t(-Δ)a and L2-norms.A new concise method was established to get the better decay rate in L2 (R3 ), which avoided using the Fourier splitting technique completely and a rough decay estimates of ‖ ▽T(t) ‖ L2.%主要在三维空间中,利用半群算子e-t(-Δ)α和L2模的性质,讨论由达西法则建立的不可压渗流方程解的衰减速率.通过不完全采用傅里叶分析的方法和‖▽T(t)‖Lz的粗略估计,在L2(R3)空间中得到方程较好的衰减估计.