论文标题
非负单独的变量解针对具有空间依赖性非线性源的多孔培养基方程的不存在
Non-existence of nonnegative separate variable solutions to a porous medium equation with spatially dependent nonlinear source
论文作者
论文摘要
不存在的非负责任的经典解决方案不存在$$-ΔV（x） - | | x |^σv（x） + \ frac {v^{1/m} {1/m}（x）} {m-1} = 0，\ qquad x \ in \ qquad x \ in \ n \ in \ n \ n \ n \ n \ n \ n \ n \ n \ n \ n \ n \ n \ mathbb {r}被证明是$σ$足够大。更准确地说，在尺寸$ n \ geq4 $中，确定了$σ$的最佳下限，即确定$σ$，即$$σ\geqσ_c：= \ frac {2（m-1）（n-1）（n-1）} {3m+1} {3m+1}，$ nif，$ n \ nim $ n \ in $ n \ in $ n \ in $ n \ in \ in \ in \ in \ in \ 3,3,3,3,2,2,2,2,2,2,2,2,2,2,2,2,2,2 o c {1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2，222改进了文献中已经建立的以前的研究。该结果的副产品是针对具有空间依赖性超线性源的多孔方程培养基方程的非阴性紧凑型单独的变量溶液的不存在。
The non-existence of nonnegative compactly supported classical solutions to $$- ΔV(x) - |x|^σV(x) + \frac{V^{1/m}(x)}{m-1} = 0, \qquad x\in\mathbb{R}^N,$$ with $m>1$, $σ>0$, and $N\ge 1$, is proven for $σ$ sufficiently large. More precisely, in dimension $N\geq4$, the optimal lower bound on $σ$ for non-existence is identified, namely $$σ\geqσ_c := \frac{2(m-1)(N-1)}{3m+1},$$ while, in dimensions $N\in\{1,2,3\}$, the lower bound derived on $σ$ improves previous ones already established in the literature. A by-product of this result is the non-existence of nonnegative compactly supported separate variable solutions to a porous equation medium equation with spatially dependent superlinear source.
