论文标题
非本地时间分数p-laplacian反应扩散方程的全局界限和合同效应
Global boundedness and Allee effect for a nonlocal time fractional p-Laplacian reaction-diffusion equation
论文作者
论文摘要
研究了全局界限和渐近行为，用于非局部时间分数P-laplacian反应扩散方程（ntfplrde）$ \ frac {\ partial^{α} {α} u} {\ partial^{\ partial^{\ partial^{\ partial t^{α}}} = ex} = f uc -γu，\ qquad（x，t）\ in \ mathbb {r}^{n} \ times（0，+\ infty）$$，$ 0 <α<1，β，β，μ，k> 0，n \ leq 2 $和$δ__{p} \ right |^{p-2} \ bigtriangledown u）$。根据$ j $的适当假设和$ 1 <p <2 $的条件，证明对于任何非负和有限的初始条件，如果$ k^{*} = 0 $ for $ n = 1 $ n = 1 $ n = 1 $或$ k^{*} =（μc^} =（μc^{2}} $ {$ n = $ {gn} $ {gn} $ {gn} $ {gn} $ {gn}+for $ k^{*} = 0 $ for $ k^{*} = 0 $，则该问题具有全球有限的经典解决方案。 $ c_ {gn} $是Gagliardo-Nirenberg不等式中的常数。对于初始基准的进一步假设，对于小$μ$值，该解决方案被证明将$ 0 $指数或本地均匀地汇总为$ t \ rightarrow \ infty $，在Caputo衍生物方面被称为Allee效应。此外，在$ j \等价1 $的条件下，事实证明，非线性ntfplrde在任何维空间中都具有全球界面解决方案，其非线性p-laplacian扩散术语$δ_{p} p} p} u^{m} {m}
The global boundedness and asymptotic behavior are investigated for the solutions of a nonlocal time fractional p-Laplacian reaction-diffusion equation (NTFPLRDE) $$ \frac{\partial^{α}u}{\partial t^{α}}=Δ_{p} u+μu^{2}(1-kJ*u) -γu, \qquad(x,t)\in\mathbb{R}^{N}\times(0,+\infty)$$ with $0<α<1,β, μ,k>0,N\leq 2$ and $Δ_{p}u =div(\left| \bigtriangledown u \right|^{p-2}\bigtriangledown u)$. Under appropriate assumptions on $J$ and the conditions of $1<p<2$, it is proved that for any nonnegative and bounded initial conditions, the problem has a global bounded classical solution if $k^{*}=0$ for $N=1$ or $k^{*}=(μC^{2}_{GN}+1)η^{-1}$ for $N=2$, where $C_{GN}$ is the constant in Gagliardo-Nirenberg inequality. With further assumptions on the initial datum, for small $μ$ values, the solution is shown to converge to $0$ exponentially or locally uniformly as $t \rightarrow \infty$, which is referred as the Allee effect in sense of Caputo derivative. Moreover, under the condition of $J \equiv 1$, it is proved that the nonlinear NTFPLRDE has a global bounded solution in any dimensional space with the nonlinear p-Laplacian diffusion terms $Δ_{p} u^{m}\, (2-\frac{2}{N}< m\leq 3)$.
