论文标题
与记忆的不均匀热方程式的衰减/增长率。小尺寸的情况
Decay/growth rates for inhomogeneous heat equations with memory. The case of small dimensions
论文作者
论文摘要
我们研究了所有$ l^p $解决方案规范的衰减/增长率，以$ \ mathbb {r}^n $涉及caputo $α$α$ - 时间衍生物和功率$β$的laplacian的功率$β$在空间尺寸很小的$ 1 \ le 4 \ le n n prove时，caputo $α$ time $β$涉及caputo $α$ time $β$的衰减/增长率。费率不仅取决于$ p $，还取决于时空量表以及强迫术语的空间$ l^1 $规范的时间行为。
We study the decay/growth rates in all $L^p$ norms of solutions to an inhomogeneous nonlocal heat equation in $\mathbb{R}^N$ involving a Caputo $α$-time derivative and a power $β$ of the Laplacian when the spatial dimension is small, $1\le N\le 4β$, thus completing the already available results for large spatial dimensions. Rates depend not only on $p$, but also on the space-time scale and on the time behavior of the spatial $L^1$ norm of the forcing term.
