论文标题
在完整的Riemannian歧管上的Biharmonic热方程式上
On the biharmonic heat equation on complete Riemannian manifolds
论文作者
论文摘要
我们研究了没有边界的完整riemannian歧管上的双旋量热方程的整个解。我们提供了关于RICCI曲率下限和单位球的非碰撞的假设，为Biharmonic热核提供了指数衰减估计值。我们证明了凯奇问题的独特标准。作为推论，我们证明了Biharmonic Heat内核的保护定律，以及从有限的初始数据开始的整个溶液的均匀L量估计。
We study entire solutions of the biharmonic heat equation on complete Riemannian manifolds without boundary. We provide exponential decay estimates for the biharmonic heat kernel under assumptions on the lower bound of Ricci curvature and noncollapsing of unit balls. And we prove a uniqueness criteria for the Cauchy problem. As corollaries we prove the conservation law for the biharmonic heat kernel and a uniform L-infinite estimate for entire solutions starting with bounded initial data.
