A Note on Evolution Equation on Manifold

In the present paper, considering the differential equations on smooth closed manifolds, we investigate and establish the well-posedness of boundary value problems nonlocal type for parabolic equations and also hyperbolic equations in Hölder spaces. Furthermore, in various Hölder norms we establish new coercivity estimates for the solutions of such type parabolic boundary value problems on manifolds and hyperbolic boundary value problems on manifolds as well.