论文标题
cauchy问题的渐近特性对于歧管上不均匀密度的退化抛物线方程
Asymptotic properties of solutions to the Cauchy problem for degenerate parabolic equations with inhomogeneous density on manifolds
论文作者
论文摘要
我们考虑了双线非线性退化抛物线方程的库奇问题，其在非伴随riemannian歧管上的密度不均匀。我们对问题解决方案的行为进行定性分类，具体取决于无穷大的密度函数的行为和歧管的几何形状，这是根据其等速函数描述的。我们为解决方案的属性确定：在很大程度上稳定溶液对零的稳定，有限的传播速度，溶液的通用界限，爆炸的界面。这些行为中的每一种当然都在适当的参数范围内进行，其定义涉及通用的几何特征函数，这取决于歧管的几何形状和无穷大密度的渐近学。
We consider the Cauchy problem for doubly nonlinear degenerate parabolic equations with inhomogeneous density on noncompact Riemannian manifolds. We give a qualitative classification of the behavior of the solutions of the problem depending on the behavior of the density function at infinity and the geometry of the manifold, which is described in terms of its isoperimetric function. We establish for the solutions properties as: stabilization of the solution to zero for large times, finite speed of propagation, universal bounds of the solution, blow up of the interface. Each one of these behaviors of course takes place in a suitable range of parameters, whose definition involves a universal geometrical characteristic function, depending both on the geometry of the manifold and on the asymptotics of the density at infinity.
