On the Biharmonic Heat Equation on Complete Riemannian Manifolds

We study entire solutions of the biharmonic heat equation on complete Riemannian manifolds without boundary. provide exponential decay estimates for kernel under assumptions lower bound Ricci curvature and noncollapsing unit balls. And we prove a uniqueness criteria Cauchy problem. As corollaries, conservation law uniform $$L^\infty $$ estimate starting with bounded initial data.