论文标题
由$ p $ -laplacian驱动的反应扩散进化方程的全球存在
Global existence for reaction-diffusion evolution equations driven by the $p$-Laplacian on manifolds
论文作者
论文摘要
我们考虑由$ p $ -laplacian驱动的反应扩散方程在非算法的无限体积歧管上，假定支持Sobolev不平等，在某些情况下，具有$ l^2 $频谱从零界定的$ l^2 $频谱，这是我们的主要示例，我们在任何维度的高度boical spectimension。结果表明，在适当的条件下，在涉及的参数和初始数据上的较小条件下，存在全局时间解决方案以及适当的平滑效果，即在$ l^q $ norms of Pative time of Positive的$ l^\ Infty $ norm of Solutions of Solutions of Solutions of Solutions of Solutions form norm norm normes norm。这里讨论的几何设置需要重大修改W.R.T.欧几里得策略。
We consider reaction-diffusion equations driven by the $p$-Laplacian on noncompact, infinite volume manifolds assumed to support the Sobolev inequality and, in some cases, to have $L^2$ spectrum bounded away from zero, the main example we have in mind being the hyperbolic space of any dimension. It is shown that, under appropriate conditions on the parameters involved and smallness conditions on the initial data, global in time solutions exist and suitable smoothing effects, namely explicit bounds on the $L^\infty$ norm of solutions at all positive times, in terms of $L^q$ norms of the data. The geometric setting discussed here requires significant modifications w.r.t. the Euclidean strategies.
