A Note on Evolution Equation on Manifold

Abstract

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 H\"{o}lder spaces. Furthermore, in various H\"{o}lder 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.