论文标题
具有较小初始能量的多孔培养基方程的长期行为
Long-time behavior for the porous medium equation with small initial energy
论文作者
论文摘要
我们研究了具有平滑边界的开放界连接集中多孔介质方程解决方案的长期行为。考虑了均匀的dirichlet边界条件。我们证明，如果初始基准的能量足够小，则溶液将收敛到均匀重新缩放的均方根泳道方程的非平凡恒定符号溶液。我们指出，允许签名的初始基准进行更改。我们还对初始基准提出了足够的能量标准，该标准允许确定融合是朝着阳性解决方案还是对负面解决方案。
We study the long-time behavior for the solution of the Porous Medium Equation in an open bounded connected set, with smooth boundary. Homogeneous Dirichlet boundary conditions are considered. We prove that if the initial datum has sufficiently small energy, then the solution converges to a nontrivial constant sign solution of a sublinear Lane-Emden equation, once suitably rescaled. We point out that the initial datum is allowed to be sign-changing. We also give a sufficient energetic criterion on the initial datum, which permits to decide whether convergence takes place towards the positive solution or to the negative one.
